Cf N 701: Fill & Download for Free

Here are some entries from Lewis and Short. If you really want to understand the areas of identity, overlap and divergence, I recommend studying each entry in its entirety. To complete the picture I included matrona, about which you didn't ask.fēmina , ae, f. from fe-, fev-, = Gr. , to produce; whence: fetus, fecundus, faenus, felix; cf. Sanscr. bhuas, bhavas, to become; Lat. fi-o, fu-turus,I. a female.I. Lit.A. Of human beings, a female, woman (cf.: uxor, mulier, matrona;“ conjux, marita): ut a prima congressione maris et feminae ... ordiar,” Cic. Rep. 1, 24:“ et mares deos et feminas esse dicitis,” id. N. D. 1, 34, 95:“ ambiguus fuerit modo vir, modo femina Sithon,” Ov. M. 4, 280; cf. Lucr. 4, 819:“ in claris viris et feminis,” Cic. Tusc. 1, 12, 27:“ pulchritudine eximiā femina,” id. Div. 1, 25, 52:“ feminae notitiam habere,” Caes. B. G. 6, 21 fin.:“ naturam feminarum omnem castitatem pati,” Cic. Leg. 2, 12, 29; cf. id. Rep. 3, 10 fin.:“ bona,” id. Phil. 3, 6, 16; cf.:“ praestantissima omnium feminarum,” id. Fam. 5, 8, 2:“ sanctissima atque optima,” id. Phil. 3, 6, 16:“ probatissima,” id. Caecin. 4, 10:“ primaria,” id. Fam. 5, 11, 2:“ decreta super jugandis feminis,” Hor. C. S. 19:“ varium et mutabile semper femina,” Verg. A. 4, 570:“ tunc femina simplex,” the female character undisguised, Juv. 6, 327.—Adj.:“ inter quas Danai femina turba senis,” Prop. 2, 31 (3, 29), 4.—Applied as a term of reproach to effeminate men, Ov. M. 12, 470; Sil. 2, 361; Suet. Caes. 22; Just. 1, 3; Curt. 3, 10 fin. al.—B. Of beasts, a female, she:“ (bestiarum) aliae mares, aliae feminae sunt,” Cic. N. D. 2, 51, 128: lupus femina feta repente, Enn. ap. Serv. Verg. A. 2, 355, and ap. Non. 378, 18 (Ann. v. 70 and 73 ed. Vahl.); cf.:“ habendas triduum ferias et porco femina piaculum pati (shortly before, porca),” Cic. Leg. 2, 22, 57:“ sus,” Col. 7, 9, 3:“ anas,” Plin. 29, 5, 33, § 104:“ anguis,” Cic. Div. 1, 18, 36; 2, 29, 62:“ piscis,” Ov. A. A. 2, 482; Plin. 9, 50, 74, § 157; Ov. M. 2, 701.—II. Transf., in the lang. of nat. hist., of plants and minerals:“ mas in palmite floret, femina citra florem germinat tantum spicae modo,” Plin. 13, 4, 7, § 31; ib. § 34;“ so of other plants,” id. 16, 33, 60, § 139; 16, 34, 62, § 145:“ 21, 10, 32, § 58 et saep.: in omni genere (carbunculorum) masculi appellantur acriores, et feminae languidius refulgentes,” Plin. 37, 7, 25, § 92;“ of the loadstone,” id. 36, 16, 25, § 128.—In mechanics, cardo femina, different from cardo masculus (v. cardo, 2), Vitr. 9, 9 med.—III. In gram., the feminine gender, Quint. 1, 6, 12; 1, 4, 24.---------------------------mŭlier , ĕris, f. mollior, comp. of mollis, q. v.,I. a woman, a female, whether married or not.I. Lit.A. In gen., Plaut. Poen. 1, 2, 36:“ mulieres omnes propter infirmitatem consilii, majores in tutorum potestate esse voluerunt,” Cic. Mur. 12, 27;“ of a virgin,” id. Verr. 2, 1, 25, § 64:“ mulieres omnes dicuntur, quaecumque sexūs feminini sunt,” Dig. 34, 2, 26:“ nil non permittit mulier sibi,” Juv. 6, 457.—B. In partic., a wife, opp. to a maid:“ ecqua virgo sit aut mulier digna, etc.,” Cic. Verr. 2, 1, 24, § 63:“ Cicero objurgantibus, quod sexagenarius Publiliam virginem duxisset, "cras mulier erit" inquit,” Quint. 6, 3, 75:“ si virgo fuit primo, postea mulier,” Lact. 1, 17, 8 al.:“ pudica mulier,” Hor. Epod. 2, 39; Suet. Vit. 2; Inscr Orell. 4661.—II. Transf., as a term of reproach, a woman, i. e. a coward, poltroon:“ non me arbitratur militem, sed mulierem,” Plaut. Bacch. 4, 8, 4.--------------------------mātrona1 , ae, f. id.,I. a married woman, wife, matron (whether she was in manu or not; consequently more general in its application than mater familias, which always denoted one who was in manu).I. In gen.: matronam dictam esse proprie, quae in matrimonium cum viro convenisset, quoad in eo matrimonio maneret, etiamsi liberi nondum nati forent: dictamque esse ita a matris nomine non adepto jam sed cum spe et omine mox adipiscendi: unde ipsum quoque matrimonium dicitur;“ matrem autem familias appellatam esse eam solam, quae in mariti manu mancipioque, aut in ejus, in cujus maritus, manu mancipicque esset: quoniam non in matrimonium tantum, sed in familiam quoque mariti, et in sui heredis locum venisset,” Gell. 18, 6, 8 and 9:“ convocatis plebeis matronis,” Liv. 10, 23, 6.—Only rarely of a married woman, woman in general:“ ut matronarum hic facta pernovit probe,” Plaut. Aul. 3, 5, 30:“ quae (dea) quia partus matronarum tueatur,” Cic. N. D. 3, 18, 47; cf.: et fetus matrona dabit, * Tib. 2, 5, 91:“ cum prole matronisque nostris,” Hor. C. 4, 15, 27:“ tyranni,” id. ib. 3, 2, 7: matronae muros complent, Enn. ap. Serv ad Verg. G. 1, 18 (Ann. v 376 Vahl.): tum muros variā cinxere coronā Matronae, * Verg. A. 11, 476: matronae tacitae spectent, tacitae rideant Plaut. Poen. prol. 32 Suet. Ner. 27:“ matronas prostratae pudicitiae,” id. Tib. 35:“ dilectae adulter matronae,” Juv. 10, 319.—II. Esp.A. The word very early acquired the accessory idea of (moral or social) dignity, rank. Matronae is thus used even by Ennius of women of quality, ladies: matronae opulentae, optimates, Enn. ap. Cic. Fam. 7, 6 (Trag. v. 294 Vahl.); cf.“ , in like manner, in Plautus: ubi istas videas summo genere natas Summates matronas,” Plaut. Cist. 1, 1, 26;“ so Cicero applies to the noble women carried off from the Sabines the term matronae,” Cic. Rep. 2, 7, 13:“ matrona laris,” the lady of the house, Juv. 3, 110.—B. With the accessory idea of estimable, virtuous, chaste, etc.: nominis matronae sanctitudinem, Afran. ap. Non. 174, 9:“ eam hic ornatam adducas ad matronarum modum,” Plaut. Mil. 3, 1, 196 Brix ad loc.; cf.:“ matronarum sanctitas,” Cic. Cael. 13, 32:“ VETERIS SANCTITATIS MATRONA,” Inscr. Orell. 2739. So opp. meretrix, Plaut. Cist. 1, 1, 80; cf. id. Most. 1, 3, 33; id. Cas. 3, 3, 22:“ ut matrona meretrici dispar erit atque Discolor,” Hor. Ep. 1, 18, 3; Plaut. Stich. 1, 2, 48:“ matronae praeter faciem nil cernere possis, etc.,” Hor. S. 1, 2, 94:“ capitis matrona pudici,” Juv. 6, 49.—C. Hence, an appellation of Juno:“ hinc matrona Juno (stetit),” Hor. C. 3, 4, 59:“ MATRONIS IVNONIBVS,” Inscr. Orell. 2085;“ and of other protecting goddesses of places,” ib. 2081 sq. (But not of vestals; v. Drak. ad Liv. 29, 14, 12.)--------------------------uxor , ōris (for the form VXSOR in inscrr.I. v. the letter X), f. etym. dub.; cf. Sanscr. vaca, wife, a wife, spouse, consort (syn. conjux).I. Lit.:“ licuit uxorem dotatam ducere,” Plaut. Mil. 3, 1, 86: duxit me uxorem liberorum sibi quaesendūm gratia, Enn. ap. Fest. s. v. quaeso, p. 258 (Trag. v. 161 Vahl.);“ so very freq. ducere uxorem, v. duco: uxorem adjungere,” Cic. Fin. 3, 20, 68:“ ridicule illud L. Nasica censori Catoni, cum ille Ex tui animi sententiā tu uxorem habes? Non hercle, inquit, ex animi mei sententiā,” id. de Or. 2, 64, 260:“ erus, quantum audio, uxore excidit,” must go without a wife, Ter. And. 2, 5, 12; 1, 3, 11:“ quod tu dicis, mea uxor, non te mihi irasci decet,” Plaut. Am. 1, 3, 24.—On the legal condition of Roman married women, v. Rein, Röm. Privatr. p. 182 sq.; Dict. of Antiq. s. v. uxor.—II. Transf.A. Of animals:“ olentis uxores mariti,” i. e. she-goats, Hor. C. 1, 17, 7.—B. Humorously, of the cloak (abolla) as inseparable from the poor man, Mart. 4, 53, 5.

There is one well-known solution for this problem [math](3, 4,5,6)[/math]:[math]3^3 +4^3 +5^3=6^3[/math] or [math](1,6,8,9)[/math] (Update: Well, they don't satisfy a rather artificial pairwise gcd condition).To describe all solutions we can make use of the underlying geometry. This equation describes the famous cubic Fermat surface [math]C[/math] in [math]\mathbf{P}^3[/math].All [math]27[/math] lines on [math]C[/math] are particularly easy to describe.Although Fermat surface has no rational pairs of skew lines, yet it still haspairs of complex conjugate ones; for example, you can choose one line in [math]\mathbf{P}^3[/math] given by [math]L: x+\varepsilon y=0, t-\varepsilon z=0[/math] and a second line given by [math]M: x+\overline{\varepsilon} y=0, [/math][math][/math][math] [/math][math][/math][math] t-\overline{\varepsilon} z=0.[/math] Here [math]\varepsilon[/math] is a primitive 3rd root of unity.This condition is sufficient (in fact, necessary as well) for existence of rational parametrization; check Page on arxiv.org §3 for a simple geometrical construction how to obtain it. The idea pertains to construction of a rational plane that contains a rational line which intersects both skew lines. A point of this rational planes uniquely defines a point on [math]C[/math] by constructing the unique line through this point meeting both skew lines. I this way one gets a rational parametrization [math]\mathbf{P}^2 \to C[/math].The result is not that elegant as the above construction though.Another parametrization Complete cubic parametrization of w^3+x^3+y^3+z^3=0 uses the fact that Fermat surface (in general, a smooth cubic surface) is a blow-up of [math]\mathbf{P}^2[/math] at [math]6[/math] points. In fact, parametrization is the inverse construction (i.e. blow-down at 6 skew lines).And finally the most old and interesting rational parametrization of [math]C[/math] was found by Leonhard Euler. It makes use of polynomials of degree [math][/math][math] 4[/math] unlike two former examples, but the formula looks nice and seem to be well adjusted for search of positive quadruples:[math][/math][math] \begin{matrix} x=c^4 -c(a-3b)(a^2+3b^2) [/math][math][/math][math]\\ y=c(a+3b)(a^2 +3b^2) -c^4\\ z=(a^2 +3b^2)^2 -c^3(a+3b)\\ t=(a^2 +3b^2)^2 +(3b-a)c^3\end{matrix}[/math](cf: History of the Theory of Numbers, vol.2., pp 552-554 )However, since Euler's parametrization of degree 4 it one should probably work with rational numbers to get satisfactory (pairwise co-prime) results.The parametrization of Elkies works for this purpose much better producing loads of counterexamples:[math][/math][math] \begin{array}{ll} x=-a^3-2a^2 c +3 a^2b +12abc [/math][math][/math][math]\\ -3ab^2-4ac^2+6b^2c +12bc^2 +9b^3\\ [/math][math][/math][math]~\\ y=a^3+2a^2c +3a^2b +12abc [/math][math][/math][math]+\\ 3ab^2 [/math][math][/math][math]+ 4ac^2-6b^2c +12bc^2 +9b^3\\ [/math][math][/math][math]~\\ z=-8c^3-8ac^2-9b^3-a^3\\ -3a^2b-3ab^2-4a^2c -12b^2c\\ [/math][math][/math][math]~\\ t=-8c^3-8ac^2+9b^3-a^3+3a^2b\\ -3ab^2-4a^2c-12b^2c \end{array}[/math]The following Python code implements brute force search of counterexamples :def gcdmod(l): #gcd of numbers in the list  from fractions import gcd;  a=l[0]  for x in l:  a=gcd(a,x)  return(a) def test(l): # checks whether a guadruple admissible (pairwise prime and positive)  from fractions import gcd;  from itertools import combinations;  for x in l:  if (x<=0):  return False  y=fcdmod(l);  ld=[]  for x in l:  ld.append(x/y)  for k in combinations(ld,2):  if (gcd(k[0],k[1])>1):  return False  return(True) def generator(n): #generates quadruples and picks counterexamples out  for c in range(-n,n+1):  for a in range(-n,n+1):  for b in range(-n,n+1):  x=-a**3-2*(a**2)*c +3*(a**2)*b +12*a*b*c -3*a*(b**2)-4*a*(c**2)+6*b*b*c +12*b*(c**2) +9*(b**3);  y=a**3+2*(a**2)*c +3*(a**2)*b +12*a*b*c +3*a*(b**2) + 4*a*(c**2)-6*b*b*c +12*b*(c**2)+9*(b**3);  z=-8*c**3-8*a*(c**2)-9*b**3-a**3-3*(a**2)*b-3*a*(b**2)-4*(a**2)*c -12*(b**2)*c;  t=-(8*c**3+8*a*(c**2)-9*b**3+a**3-3*(a**2)*b+3*a*(b**2)+4*(a**2)*c+12*(b**2)*c);  res=x**3+y**3+z**3-t**3;  if test([x,y,z,t]):  m=gcdmod([x,y,z,t]);  print("(",x//m,",",y//m,",",z//m,",",t//m,")"); Results (counterexamples/solutions)>>> generator(20) ( 3989 , 877 , 5983 , 6529 ) ( 41779 , 19043 , 49877 , 58859 ) ( 65077 , 49253 , 54227 , 82157 ) ( 44923 , 32861 , 46619 , 61043 ) ( 69229 , 66887 , 50033 , 91109 ) ( 14311 , 851 , 35429 , 36191 ) ( 29257 , 20117 , 39203 , 45377 ) ( 4733 , 4063 , 5197 , 6793 ) ( 383 , 379 , 349 , 535 ) ( 31441 , 31943 , 36977 , 48521 ) ( 51067 , 63449 , 40031 , 76787 ) ( 1667 , 1399 , 3541 , 3727 ) ( 19063 , 20159 , 30521 , 35183 ) ( 33433 , 44897 , 34583 , 55313 ) ( 3019 , 5807 , 19913 , 20099 ) ( 1931 , 3697 , 3163 , 4471 ) ( 21319 , 42251 , 26669 , 47039 ) ( 4003 , 11993 , 18527 , 20123 ) ( 11029 , 28739 , 21941 , 32909 ) ( 22591 , 56501 , 22979 , 58871 ) ( 109 , 437 , 293 , 479 ) ( 11101 , 39869 , 19451 , 41621 ) ( 2099 , 6883 , 2377 , 7039 ) ( 2347 , 38183 , 12497 , 38627 ) ( 1699 , 52337 , 6983 , 52379 ) ( 48365 , 16561 , 52333 , 63907 ) ( 31523 , 6073 , 44581 , 49345 ) ( 78623 , 65269 , 51049 , 96445 ) ( 34715 , 18331 , 40987 , 48889 ) ( 55421 , 45949 , 44833 , 70963 ) ( 37379 , 30613 , 38281 , 51553 ) ( 59237 , 62191 , 40903 , 80251 ) ( 10991 , 1867 , 28267 , 28813 ) ( 39947 , 43783 , 35599 , 57769 ) ( 701 , 535 , 1363 , 1447 ) ( 25385 , 29359 , 29959 , 40927 ) ( 42851 , 58705 , 32077 , 67969 ) ( 5573 , 4189 , 20929 , 21115 ) ( 15527 , 27697 , 22957 , 33349 ) ( 29033 , 55243 , 24139 , 59167 ) ( 1427 , 5671 , 15343 , 15601 ) ( 16271 , 38659 , 20659 , 41389 ) ( 1931 , 10897 , 14221 , 16105 ) ( 7373 , 26059 , 16843 , 28387 ) ( 17351 , 52237 , 16657 , 53413 ) ( 1475 , 17011 , 13123 , 19297 ) ( 491 , 24877 , 11185 , 25609 ) ( 7373 , 50119 , 9199 , 50275 ) ( 13123 , 1475 , 17011 , 19297 ) ( 135665 , 46801 , 140291 , 175013 ) ( 157979 , 72955 , 143513 , 193871 ) ( 182285 , 101869 , 146567 , 217313 ) ( 238601 , 169705 , 150443 , 279677 ) ( 271475 , 209491 , 150401 , 319463 ) ( 99037 , 13751 , 130141 , 147025 ) ( 118423 , 35993 , 132955 , 159499 ) ( 161587 , 87317 , 139519 , 196615 ) ( 186229 , 117263 , 142405 , 222121 ) ( 213487 , 150641 , 144451 , 252835 ) ( 9371 , 599 , 13693 , 15023 ) ( 1627 , 415 , 1997 , 2311 ) ( 1555 , 517 , 1769 , 2113 ) ( 15833 , 8213 , 14719 , 19757 ) ( 18355 , 11311 , 15077 , 22279 ) ( 2831 , 2081 , 1933 , 3389 ) ( 24239 , 18635 , 15529 , 29027 ) ( 27697 , 22957 , 15527 , 33349 ) ( 3697 , 3163 , 1931 , 4471 ) ( 87803 , 17209 , 118907 , 133199 ) ( 168851 , 116497 , 131939 , 205607 ) ( 27779 , 21277 , 19151 , 33647 ) ( 255089 , 225991 , 133901 , 312581 ) ( 74233 , 9137 , 112291 , 122221 ) ( 10313 , 2341 , 14201 , 15839 ) ( 108757 , 50381 , 118567 , 145513 ) ( 14771 , 7759 , 15047 , 19217 ) ( 127999 , 74423 , 122173 , 163027 ) ( 2867 , 2071 , 2267 , 3533 ) ( 172603 , 131507 , 128161 , 211951 ) ( 198829 , 165413 , 129679 , 244225 ) ( 12013 , 10709 , 6823 , 14857 ) ( 2867 , 745 , 4019 , 4463 ) ( 4853 , 3235 , 4409 , 6161 ) ( 7183 , 461 , 12625 , 13357 ) ( 11041 , 5111 , 13375 , 15703 ) ( 96659 , 51463 , 108845 , 132551 ) ( 114437 , 74521 , 112571 , 149465 ) ( 15499 , 10889 , 14293 , 19945 ) ( 134063 , 100483 , 115985 , 170819 ) ( 20989 , 18227 , 14947 , 26515 ) ( 180587 , 162847 , 120149 , 228575 ) ( 208349 , 200113 , 120035 , 265841 ) ( 1723 , 173 , 3103 , 3271 ) ( 67807 , 22517 , 98911 , 108883 ) ( 82945 , 41519 , 102373 , 119701 ) ( 99259 , 62801 , 106147 , 134287 ) ( 117181 , 86795 , 109801 , 153073 ) ( 159577 , 144647 , 115021 , 204973 ) ( 213589 , 218531 , 114577 , 278857 ) ( 293 , 109 , 437 , 479 ) ( 3163 , 1931 , 3697 , 4471 ) ( 5197 , 4733 , 4063 , 6793 ) ( 45827 , 8341 , 87167 , 91223 ) ( 58949 , 24463 , 90053 , 98297 ) ( 72767 , 42481 , 93635 , 108659 ) ( 87713 , 62827 , 97481 , 122741 ) ( 104219 , 85933 , 101159 , 140975 ) ( 17531 , 16033 , 14891 , 23399 ) ( 143639 , 142153 , 106283 , 191627 ) ( 194483 , 214597 , 105551 , 264071 ) ( 61261 , 33785 , 87643 , 98017 ) ( 8495 , 5353 , 11189 , 12941 ) ( 10705 , 7493 , 13063 , 15709 ) ( 1751 , 1525 , 1733 , 2417 ) ( 106675 , 97919 , 98677 , 146023 ) ( 4321 , 1207 , 8765 , 9109 ) ( 209 , 107 , 337 , 365 ) ( 7037 , 4787 , 9505 , 10961 ) ( 379 , 349 , 383 , 535 ) ( 1733 , 1751 , 1525 , 2417 ) ( 14293 , 15499 , 10889 , 19945 ) ( 5869 , 3329 , 9757 , 10531 ) ( 52811 , 34675 , 79841 , 88703 ) ( 65213 , 52453 , 83663 , 100241 ) ( 691 , 599 , 823 , 1033 ) ( 94265 , 96289 , 90803 , 135341 ) ( 12841 , 13661 , 11521 , 18367 ) ( 111779 , 123211 , 93257 , 159767 ) ( 131861 , 154045 , 94391 , 189353 ) ( 154943 , 189223 , 93773 , 224531 ) ( 32551 , 12977 , 71299 , 73627 ) ( 43273 , 27179 , 74377 , 80029 ) ( 66949 , 61991 , 81901 , 102841 ) ( 114523 , 136709 , 90127 , 168559 ) ( 159319 , 206561 , 88531 , 238411 ) ( 911 , 283 , 2465 , 2507 ) ( 2081 , 1933 , 2831 , 3389 ) ( 349 , 383 , 379 , 535 ) ( 3659 , 4471 , 3173 , 5543 ) ( 17291 , 3025 , 62243 , 62687 ) ( 26765 , 14731 , 64361 , 66113 ) ( 36359 , 28045 , 67463 , 72251 ) ( 46505 , 43399 , 71117 , 81533 ) ( 70181 , 81955 , 78353 , 111257 ) ( 84575 , 106021 , 81071 , 132563 ) ( 101249 , 133855 , 82613 , 158741 ) ( 1889 , 529 , 7373 , 7415 ) ( 19603 , 9683 , 59905 , 60679 ) ( 4139 , 3547 , 8027 , 8585 ) ( 47809 , 51713 , 69715 , 83701 ) ( 58987 , 70571 , 73321 , 98335 ) ( 5521 , 7121 , 5875 , 9013 ) ( 1409 , 1873 , 1385 , 2291 ) ( 103897 , 147737 , 79099 , 169165 ) ( 124099 , 181763 , 77905 , 203191 ) ( 1111 , 1061 , 2263 , 2419 ) ( 319 , 425 , 379 , 547 ) ( 6983 , 1699 , 52337 , 52379 ) ( 2377 , 2099 , 6883 , 7039 ) ( 22979 , 22591 , 56501 , 58871 ) ( 40031 , 51067 , 63449 , 76787 ) ( 50033 , 69229 , 66887 , 91109 ) ( 75149 , 115561 , 71531 , 132641 ) ( 10351 , 16193 , 8989 , 18253 ) ( 15073 , 24587 , 8587 , 26647 ) ( 9199 , 7373 , 50119 , 50275 ) ( 16657 , 17351 , 52237 , 53413 ) ( 24139 , 29033 , 55243 , 59167 ) ( 32077 , 42851 , 58705 , 67969 ) ( 40903 , 59237 , 62191 , 80251 ) ( 51049 , 78623 , 65269 , 96445 ) ( 77029 , 128123 , 68473 , 142297 ) ( 421 , 445 , 5207 , 5209 ) ( 103 , 115 , 659 , 661 ) ( 5717 , 9127 , 44909 , 45065 ) ( 12239 , 18313 , 46955 , 48131 ) ( 18737 , 29251 , 49841 , 53765 ) ( 25643 , 42373 , 53135 , 62399 ) ( 42407 , 76897 , 59219 , 90395 ) ( 907 , 6047 , 41941 , 41983 ) ( 7165 , 14129 , 43363 , 43921 ) ( 1271 , 2341 , 5561 , 5717 ) ( 13159 , 23771 , 45817 , 48187 ) ( 19321 , 35405 , 48871 , 55213 ) ( 2825 , 5263 , 6311 , 7487 ) ( 26083 , 49463 , 52093 , 65431 ) ( 33877 , 66377 , 55051 , 79273 ) ( 4787 , 9505 , 7037 , 10961 ) ( 43135 , 86579 , 57313 , 97171 ) ( 54289 , 110501 , 58447 , 119557 ) ( 7589 , 15499 , 7307 , 16571 ) ( 84013 , 171233 , 55603 , 179521 ) ( 11663 , 23677 , 6689 , 24749 ) ( 509 , 1087 , 1661 , 1817 ) ( 1423 , 3671 , 5311 , 5869 ) ( 14039 , 35143 , 43949 , 50795 ) ( 2831 , 6943 , 6701 , 8699 ) ( 34757 , 84661 , 51455 , 92249 ) ( 4939 , 11987 , 6499 , 12841 ) ( 44783 , 108127 , 52181 , 114371 ) ( 10301 , 24013 , 6911 , 24809 ) ( 4435 , 19781 , 37711 , 39463 ) ( 9109 , 29375 , 40213 , 45001 ) ( 26731 , 73565 , 47863 , 80767 ) ( 5035 , 13553 , 7003 , 14359 ) ( 19 , 599 , 1285 , 1327 ) ( 517 , 1769 , 1555 , 2113 ) ( 107 , 337 , 209 , 365 ) ( 4787 , 29377 , 35891 , 41543 ) ( 8885 , 40699 , 38393 , 49961 ) ( 13679 , 54781 , 40727 , 61667 ) ( 19601 , 72055 , 42461 , 77093 ) ( 36557 , 117907 , 42401 , 120833 ) ( 63209 , 181711 , 34757 , 184637 ) ( 1009 , 24761 , 32731 , 36901 ) ( 341 , 3673 , 4229 , 5003 ) ( 8461 , 46997 , 37279 , 53857 ) ( 1343 , 6787 , 4787 , 7517 ) ( 13303 , 62399 , 39157 , 67339 ) ( 27379 , 103931 , 39961 , 106471 ) ( 50191 , 162647 , 33949 , 164707 ) ( 443 , 4469 , 3775 , 5231 ) ( 877 , 5983 , 3989 , 6529 ) ( 2153 , 10139 , 4153 , 10397 ) ( 3091 , 12877 , 4007 , 13063 ) ( 5807 , 19913 , 3019 , 20099 ) ( 23 , 4915 , 4409 , 5891 ) ( 205 , 5003 , 3979 , 5731 ) ( 3275 , 46351 , 32741 , 51263 ) ( 7229 , 61345 , 34163 , 64721 ) ( 1207 , 8765 , 4321 , 9109 ) ( 2953 , 14375 , 4111 , 14527 ) ( 28451 , 128935 , 31373 , 130007 ) ( 40085 , 160441 , 26651 , 161513 ) ( 12079 , 89813 , 31615 , 91171 ) ( 2791 , 16313 , 4243 , 16435 ) ( 437 , 3733 , 1031 , 3761 ) ( 115 , 659 , 103 , 661 ) ( 5141 , 88687 , 25829 , 89417 ) ( 11663 , 112849 , 23267 , 113219 ) ( 31979 , 175501 , 11591 , 175871 ) ( 4573 , 99737 , 21691 , 100081 ) ( 983 , 14041 , 2501 , 14069 ) ( 11719 , 126083 , 17809 , 126235 ) ( 1123 , 8279 , 613 , 8287 ) ( 3401 , 21859 , 947 , 21887 ) ( 445 , 5207 , 421 , 5209 ) ( 3917 , 125317 , 10799 , 125345 ) ( 991 , 17531 , 955 , 17533 ) ( 12599 , 156463 , 3845 , 156491 ) ( 3925 , 140039 , 3853 , 140041 ) ( 30661 , 4343 , 38531 , 44159 ) ( 76897 , 59219 , 42407 , 90395 ) ( 33661 , 15713 , 34913 , 43895 ) ( 20803 , 7001 , 28937 , 32261 ) ( 10993 , 785 , 23729 , 24491 ) ( 13129 , 8339 , 21479 , 23363 ) ( 24835 , 25877 , 24749 , 36293 ) ( 42373 , 53135 , 25643 , 62399 ) ( 2071 , 2267 , 2867 , 3533 ) ( 26779 , 36791 , 22403 , 43133 ) ( 15529 , 24239 , 18635 , 29027 ) ( 29251 , 49841 , 18737 , 53765 ) ( 7759 , 15047 , 14771 , 19217 ) ( 16657 , 34313 , 16313 , 36683 ) ( 2605 , 8783 , 11243 , 12839 ) ( 7975 , 22577 , 13361 , 24329 ) ( 18313 , 46955 , 12239 , 48131 ) ( 2341 , 14201 , 10313 , 15839 ) ( 8287 , 32243 , 10631 , 32801 ) ( 1741 , 21323 , 8495 , 21767 ) ( 9127 , 44909 , 5717 , 45065 ) ( 3775 , 443 , 4469 , 5231 ) ( 39311 , 13735 , 36793 , 48367 ) ( 9505 , 7037 , 4787 , 10961 ) ( 42359 , 25633 , 33343 , 50647 ) ( 66377 , 55051 , 33877 , 79273 ) ( 4471 , 3173 , 3659 , 5543 ) ( 45599 , 38131 , 30061 , 56191 ) ( 16475 , 7009 , 22783 , 25531 ) ( 29837 , 24907 , 25621 , 38893 ) ( 49463 , 52093 , 26083 , 65431 ) ( 8249 , 1513 , 18295 , 18841 ) ( 1621 , 941 , 2435 , 2693 ) ( 18227 , 14947 , 20989 , 26515 ) ( 383 , 379 , 349 , 535 ) ( 5263 , 6311 , 2825 , 7487 ) ( 1415 , 1117 , 2371 , 2599 ) ( 35405 , 48871 , 19321 , 55213 ) ( 4007 , 3091 , 12877 , 13063 ) ( 10889 , 14293 , 15499 , 19945 ) ( 1933 , 2831 , 2081 , 3389 ) ( 21443 , 33487 , 17041 , 37411 ) ( 11633 , 21799 , 14137 , 24529 ) ( 23771 , 45817 , 13159 , 48187 ) ( 893 , 3973 , 8923 , 9181 ) ( 355 , 983 , 1241 , 1427 ) ( 5111 , 13375 , 11041 , 15703 ) ( 12569 , 31201 , 11647 , 32377 ) ( 2341 , 5561 , 1271 , 5717 ) ( 1013 , 7783 , 8185 , 10069 ) ( 5087 , 20281 , 9511 , 21055 ) ( 14129 , 43363 , 7165 , 43921 ) ( 461 , 12625 , 7183 , 13357 ) ( 283 , 2465 , 911 , 2507 ) ( 6047 , 41941 , 907 , 41983 ) ( 607 , 11 , 751 , 865 ) ( 92117 , 19057 , 95273 , 118247 ) ( 109631 , 38491 , 97079 , 131801 ) ( 18407 , 8587 , 14123 , 21317 ) ( 78763 , 11561 , 89809 , 106693 ) ( 112519 , 49541 , 93589 , 133249 ) ( 178453 , 125771 , 96199 , 204583 ) ( 237649 , 194471 , 90859 , 278179 ) ( 84011 , 31237 , 83093 , 106181 ) ( 100253 , 50287 , 85283 , 120623 ) ( 118343 , 71809 , 87161 , 139073 ) ( 188021 , 155527 , 86603 , 222791 ) ( 217823 , 191257 , 82913 , 261593 ) ( 57991 , 7739 , 75991 , 85921 ) ( 86467 , 40919 , 80251 , 107197 ) ( 102901 , 60713 , 82417 , 123271 ) ( 193357 , 171329 , 81241 , 233887 ) ( 50189 , 10141 , 68189 , 76319 ) ( 76169 , 41497 , 72833 , 96539 ) ( 175979 , 168187 , 73943 , 219749 ) ( 11191 , 7229 , 10081 , 14101 ) ( 93739 , 70493 , 72637 , 115909 ) ( 4787 , 1343 , 6787 , 7517 ) ( 823 , 691 , 599 , 1033 ) ( 15047 , 14771 , 7759 , 19217 ) ( 2669 , 523 , 4367 , 4679 ) ( 45011 , 19393 , 58937 , 67181 ) ( 68591 , 50269 , 64061 , 89321 ) ( 14141 , 13087 , 9623 , 18131 ) ( 117821 , 117283 , 67247 , 152591 ) ( 164921 , 180799 , 61331 , 219851 ) ( 27103 , 2183 , 52747 , 55033 ) ( 293 , 109 , 437 , 479 ) ( 46747 , 26627 , 57103 , 67477 ) ( 57901 , 41621 , 59749 , 78271 ) ( 70519 , 59039 , 62131 , 92689 ) ( 6541 , 6101 , 4909 , 8551 ) ( 121477 , 130157 , 63373 , 162007 ) ( 144271 , 161591 , 60379 , 195241 ) ( 22277 , 4201 , 46769 , 48407 ) ( 30767 , 14803 , 48767 , 52937 ) ( 5687 , 3859 , 7331 , 8597 ) ( 74567 , 77611 , 57959 , 102497 ) ( 108419 , 127303 , 57227 , 152189 ) ( 16123 , 449 , 43321 , 44053 ) ( 41161 , 33767 , 49963 , 61531 ) ( 51283 , 48857 , 52513 , 73453 ) ( 63013 , 66659 , 54511 , 89143 ) ( 134653 , 173627 , 48343 , 198223 ) ( 12497 , 2347 , 38183 , 38627 ) ( 19451 , 11101 , 39869 , 41621 ) ( 26669 , 21319 , 42251 , 47039 ) ( 34583 , 33433 , 44897 , 55313 ) ( 349 , 383 , 379 , 535 ) ( 54227 , 65077 , 49253 , 82157 ) ( 81839 , 109489 , 49481 , 125609 ) ( 99713 , 137563 , 46967 , 154643 ) ( 967 , 1361 , 337 , 1513 ) ( 20659 , 16271 , 38659 , 41389 ) ( 35599 , 39947 , 43783 , 57769 ) ( 44833 , 55421 , 45949 , 70963 ) ( 103609 , 151637 , 41893 , 167179 ) ( 1031 , 437 , 3733 , 3761 ) ( 3173 , 3659 , 4471 , 5543 ) ( 4063 , 5197 , 4733 , 6793 ) ( 1087 , 1661 , 509 , 1817 ) ( 11993 , 18527 , 4003 , 20123 ) ( 10631 , 8287 , 32243 , 32801 ) ( 16313 , 16657 , 34313 , 36683 ) ( 22403 , 26779 , 36791 , 43133 ) ( 47441 , 71977 , 42353 , 82211 ) ( 74093 , 118789 , 40181 , 129023 ) ( 11647 , 12569 , 31201 , 32377 ) ( 17041 , 21443 , 33487 , 37411 ) ( 30061 , 45599 , 38131 , 56191 ) ( 6991 , 11597 , 5713 , 12781 ) ( 61651 , 104333 , 38797 , 112621 ) ( 95791 , 163529 , 30001 , 174121 ) ( 1187 , 1861 , 3929 , 4097 ) ( 40919 , 79117 , 35213 , 84689 ) ( 52553 , 101911 , 33659 , 107483 ) ( 4747 , 9851 , 24919 , 25477 ) ( 8797 , 16973 , 26797 , 29167 ) ( 32437 , 68261 , 33109 , 72967 ) ( 4213 , 8741 , 2269 , 9103 ) ( 5531 , 16999 , 23531 , 26261 ) ( 13367 , 36259 , 27311 , 41297 ) ( 18761 , 49813 , 28517 , 53531 ) ( 60257 , 140269 , 18701 , 143987 ) ( 2521 , 13631 , 21139 , 22891 ) ( 5539 , 20849 , 22921 , 27709 ) ( 9013 , 30203 , 24727 , 35143 ) ( 107 , 337 , 209 , 365 ) ( 19057 , 57047 , 26683 , 59587 ) ( 26491 , 75401 , 25969 , 77461 ) ( 36109 , 97619 , 23551 , 99679 ) ( 48343 , 124133 , 18997 , 126673 ) ( 509 , 1243 , 95 , 1271 ) ( 281 , 1889 , 2281 , 2651 ) ( 109 , 437 , 293 , 479 ) ( 1487 , 5399 , 2731 , 5657 ) ( 5671 , 15343 , 1427 , 15601 ) ( 5027 , 29581 , 21389 , 32957 ) ( 8597 , 41143 , 22427 , 43367 ) ( 13439 , 55753 , 22577 , 57209 ) ( 39917 , 122191 , 13379 , 123647 ) ( 54167 , 153313 , 5657 , 155537 ) ( 1873 , 24629 , 19141 , 28003 ) ( 4309 , 15377 , 1933 , 15499 ) ( 641 , 34081 , 16889 , 35411 ) ( 3659 , 46699 , 16871 , 47429 ) ( 8093 , 62653 , 15677 , 63023 ) ( 115 , 659 , 103 , 661 ) ( 22937 , 106297 , 8033 , 106667 ) ( 34211 , 134851 , 719 , 135581 ) ( 8149 , 71567 , 12163 , 71719 ) ( 15103 , 93281 , 8089 , 93433 ) ( 2731 , 81059 , 2671 , 81061 ) ( 3457 , 515 , 3737 , 4541 ) ( 41017 , 22367 , 27557 , 46589 ) ( 15901 , 5567 , 18821 , 22145 ) ( 6943 , 6701 , 2831 , 8699 ) ( 8131 , 695 , 14957 , 15719 ) ( 425 , 379 , 319 , 547 ) ( 9643 , 6353 , 13331 , 15215 ) ( 19261 , 20507 , 15305 , 26849 ) ( 35143 , 43949 , 14039 , 50795 ) ( 4153 , 2153 , 10139 , 10397 ) ( 1525 , 1733 , 1751 , 2417 ) ( 3671 , 5311 , 1423 , 5869 ) ( 5353 , 11189 , 8495 , 12941 ) ( 1061 , 2263 , 1111 , 2419 ) ( 1861 , 3929 , 1187 , 4097 ) ( 5665 , 17399 , 6989 , 17957 ) ( 11 , 751 , 607 , 865 ) ( 121 , 2351 , 461 , 2357 ) ( 19391 , 4093 , 20269 , 25033 ) ( 12293 , 5431 , 14251 , 16999 ) ( 23423 , 19801 , 15793 , 29065 ) ( 13661 , 11521 , 12841 , 18367 ) ( 15077 , 18355 , 11311 , 22279 ) ( 29375 , 40213 , 9109 , 45001 ) ( 599 , 823 , 691 , 1033 ) ( 16973 , 26797 , 8797 , 29167 ) ( 3209 , 5587 , 6607 , 7915 ) ( 8579 , 16789 , 7573 , 17965 ) ( 19781 , 37711 , 4435 , 39463 ) ( 3329 , 9757 , 5869 , 10531 ) ( 9851 , 24919 , 4747 , 25477 ) ( 359 , 5269 , 4117 , 6001 ) ( 269 , 1195 , 319 , 1207 ) ( 8185 , 1013 , 7783 , 10069 ) ( 1241 , 355 , 983 , 1427 ) ( 86981 , 30685 , 63227 , 97949 ) ( 9413 , 5245 , 4859 , 10301 ) ( 2371 , 1415 , 1117 , 2599 ) ( 2435 , 1621 , 941 , 2693 ) ( 168605 , 117301 , 58403 , 187637 ) ( 22783 , 16475 , 7009 , 25531 ) ( 196871 , 147295 , 53177 , 222239 ) ( 61153 , 9299 , 58693 , 75577 ) ( 74491 , 23477 , 59491 , 86035 ) ( 89437 , 39503 , 60169 , 99829 ) ( 148243 , 102989 , 57163 , 165547 ) ( 203407 , 162473 , 46639 , 233959 ) ( 53087 , 11317 , 52067 , 66359 ) ( 65249 , 24655 , 53129 , 76217 ) ( 78971 , 39889 , 54023 , 89363 ) ( 112823 , 77773 , 53579 , 127247 ) ( 133817 , 101287 , 51377 , 152849 ) ( 158099 , 128425 , 47279 , 183467 ) ( 186101 , 159619 , 40853 , 219533 ) ( 607 , 11 , 751 , 865 ) ( 54967 , 18407 , 49585 , 66511 ) ( 81331 , 48227 , 51445 , 92299 ) ( 13939 , 9539 , 7333 , 15835 ) ( 13331 , 9643 , 6353 , 15215 ) ( 138337 , 113297 , 46855 , 161401 ) ( 18821 , 15901 , 5567 , 22145 ) ( 3979 , 205 , 5003 , 5731 ) ( 6311 , 2825 , 5263 , 7487 ) ( 11189 , 8495 , 5353 , 12941 ) ( 13375 , 11041 , 5111 , 15703 ) ( 1769 , 1555 , 517 , 2113 ) ( 4117 , 359 , 5269 , 6001 ) ( 37547 , 8023 , 42689 , 50819 ) ( 6607 , 3209 , 5587 , 7915 ) ( 58631 , 32467 , 45317 , 69023 ) ( 5501 , 3673 , 3551 , 6389 ) ( 86531 , 65647 , 46121 , 100955 ) ( 8009 , 6661 , 3443 , 9473 ) ( 14251 , 12293 , 5431 , 16999 ) ( 124703 , 111019 , 41645 , 150071 ) ( 20269 , 19391 , 4093 , 25033 ) ( 30217 , 3791 , 39433 , 44641 ) ( 39139 , 14033 , 40711 , 50683 ) ( 60511 , 39629 , 43339 , 71479 ) ( 107869 , 97283 , 40981 , 130933 ) ( 154681 , 153599 , 30169 , 194449 ) ( 25223 , 5329 , 34439 , 38495 ) ( 33161 , 14827 , 35885 , 44129 ) ( 42083 , 25933 , 37451 , 52475 ) ( 96251 , 95077 , 36275 , 121619 ) ( 116573 , 120703 , 31961 , 150005 ) ( 19429 , 1865 , 31567 , 33853 ) ( 2867 , 745 , 4019 , 4463 ) ( 34465 , 20261 , 34483 , 44857 ) ( 4853 , 3235 , 4409 , 6161 ) ( 43531 , 32015 , 35977 , 54499 ) ( 54205 , 46049 , 36919 , 67477 ) ( 66919 , 62795 , 36877 , 84223 ) ( 11345 , 11743 , 4253 , 14669 ) ( 121621 , 133625 , 26527 , 161389 ) ( 293 , 109 , 437 , 479 ) ( 21941 , 11029 , 28739 , 32909 ) ( 3163 , 1931 , 3697 , 4471 ) ( 36977 , 31441 , 31943 , 48521 ) ( 5197 , 4733 , 4063 , 6793 ) ( 46619 , 44923 , 32861 , 61043 ) ( 8119 , 8807 , 4021 , 10867 ) ( 72311 , 80599 , 31169 , 97679 ) ( 109427 , 130771 , 21893 , 152651 ) ( 1889 , 2281 , 281 , 2651 ) ( 11185 , 491 , 24877 , 25609 ) ( 16843 , 7373 , 26059 , 28387 ) ( 22957 , 15527 , 27697 , 33349 ) ( 29959 , 25385 , 29359 , 40927 ) ( 38281 , 37379 , 30613 , 51553 ) ( 3973 , 4763 , 1453 , 5581 ) ( 93409 , 115355 , 22909 , 133177 ) ( 114811 , 144509 , 15643 , 165523 ) ( 209 , 107 , 337 , 365 ) ( 379 , 319 , 425 , 547 ) ( 379 , 349 , 383 , 535 ) ( 383 , 379 , 349 , 535 ) ( 4409 , 4853 , 3235 , 6161 ) ( 5587 , 6607 , 3209 , 7915 ) ( 983 , 1241 , 355 , 1427 ) ( 8783 , 11243 , 2605 , 12839 ) ( 10897 , 14221 , 1931 , 16105 ) ( 8495 , 1741 , 21323 , 21767 ) ( 13361 , 7975 , 22577 , 24329 ) ( 18635 , 15529 , 24239 , 29027 ) ( 24749 , 24835 , 25877 , 36293 ) ( 7493 , 9655 , 3761 , 11117 ) ( 66245 , 88219 , 23549 , 99677 ) ( 83039 , 112765 , 18587 , 126263 ) ( 911 , 283 , 2465 , 2507 ) ( 9511 , 5087 , 20281 , 21055 ) ( 14137 , 11633 , 21799 , 24529 ) ( 2081 , 1933 , 2831 , 3389 ) ( 349 , 383 , 379 , 535 ) ( 25621 , 29837 , 24907 , 38893 ) ( 3659 , 4471 , 3173 , 5543 ) ( 33343 , 42359 , 25633 , 50647 ) ( 42961 , 57737 , 25231 , 66025 ) ( 54907 , 76403 , 23269 , 85459 ) ( 967 , 1361 , 337 , 1513 ) ( 69613 , 98789 , 19315 , 109381 ) ( 9767 , 13939 , 2057 , 15395 ) ( 87511 , 125327 , 12937 , 138223 ) ( 461 , 121 , 2351 , 2357 ) ( 6989 , 5665 , 17399 , 17957 ) ( 1111 , 1061 , 2263 , 2419 ) ( 15305 , 19261 , 20507 , 26849 ) ( 319 , 425 , 379 , 547 ) ( 27557 , 41017 , 22367 , 46589 ) ( 6743 , 10627 , 2789 , 11519 ) ( 60875 , 96511 , 15257 , 104099 ) ( 319 , 269 , 1195 , 1207 ) ( 7573 , 8579 , 16789 , 17965 ) ( 11311 , 15077 , 18355 , 22279 ) ( 15793 , 23423 , 19801 , 29065 ) ( 49801 , 83927 , 15745 , 89569 ) ( 64483 , 107993 , 10111 , 115195 ) ( 2393 , 4099 , 13205 , 13361 ) ( 5171 , 8677 , 14387 , 15563 ) ( 8213 , 14719 , 15833 , 19757 ) ( 11951 , 22657 , 17111 , 26375 ) ( 4523 , 8881 , 2231 , 9299 ) ( 42503 , 82009 , 11903 , 85727 ) ( 56201 , 105907 , 5861 , 110945 ) ( 319 , 2603 , 11821 , 11863 ) ( 509 , 1087 , 1661 , 1817 ) ( 5371 , 11399 , 13969 , 16339 ) ( 12247 , 27011 , 16213 , 29551 ) ( 33541 , 70769 , 12199 , 73309 ) ( 4883 , 10141 , 1247 , 10511 ) ( 95 , 509 , 1243 , 1271 ) ( 337 , 967 , 1361 , 1513 ) ( 941 , 2435 , 1621 , 2693 ) ( 1399 , 3541 , 1667 , 3727 ) ( 3973 , 8923 , 893 , 9181 ) ( 599 , 1285 , 19 , 1327 ) ( 19 , 599 , 1285 , 1327 ) ( 1103 , 6583 , 10721 , 11495 ) ( 517 , 1769 , 1555 , 2113 ) ( 5387 , 17587 , 12965 , 19811 ) ( 107 , 337 , 209 , 365 ) ( 8573 , 26149 , 13619 , 27605 ) ( 13031 , 37327 , 13385 , 38399 ) ( 19193 , 51553 , 11831 , 52625 ) ( 2881 , 7493 , 1303 , 7645 ) ( 509 , 1243 , 95 , 1271 ) ( 38357 , 90877 , 3035 , 93101 ) ( 1111 , 8705 , 10327 , 12079 ) ( 415 , 1997 , 1627 , 2311 ) ( 757 , 3035 , 1741 , 3229 ) ( 20401 , 59315 , 8677 , 60169 ) ( 599 , 13693 , 9371 , 15023 ) ( 5171 , 30169 , 9599 , 30539 ) ( 23729 , 77743 , 41 , 78473 ) ( 25 , 2393 , 1231 , 2497 ) ( 2113 , 24833 , 8599 , 25177 ) ( 437 , 3733 , 1031 , 3761 ) ( 5227 , 35627 , 7597 , 35779 ) ( 115 , 659 , 103 , 661 ) ( 9949 , 49565 , 5179 , 49717 ) ( 233 , 1033 , 59 , 1037 ) ( 16711 , 67079 , 913 , 67423 ) ( 1745 , 35149 , 4619 , 35177 ) ( 445 , 5207 , 421 , 5209 ) ( 5819 , 49015 , 1697 , 49043 ) ( 1753 , 41519 , 1705 , 41521 ) ( 54781 , 40727 , 13679 , 61667 ) ( 36259 , 27311 , 13367 , 41297 ) ( 11743 , 4253 , 11345 , 14669 ) ( 22657 , 17111 , 11951 , 26375 ) ( 40699 , 38393 , 8885 , 49961 ) ( 1873 , 1385 , 1409 , 2291 ) ( 14719 , 15833 , 8213 , 19757 ) ( 29377 , 35891 , 4787 , 41543 ) ( 2731 , 1487 , 5399 , 5657 ) ( 16999 , 23531 , 5531 , 26261 ) ( 3235 , 4409 , 4853 , 6161 ) ( 8677 , 14387 , 5171 , 15563 ) ( 3547 , 8027 , 4139 , 8585 ) ( 745 , 4019 , 2867 , 4463 ) ( 4099 , 13205 , 2393 , 13361 ) ( 529 , 7373 , 1889 , 7415 ) ( 2281 , 281 , 1889 , 2651 ) ( 24587 , 8587 , 15073 , 26647 ) ( 337 , 209 , 107 , 365 ) ( 6787 , 4787 , 1343 , 7517 ) ( 27011 , 16213 , 12247 , 29551 ) ( 46997 , 37279 , 8461 , 53857 ) ( 16193 , 8989 , 10351 , 18253 ) ( 30203 , 24727 , 9013 , 35143 ) ( 8807 , 4021 , 8119 , 10867 ) ( 3989 , 877 , 5983 , 6529 ) ( 20849 , 22921 , 5539 , 27709 ) ( 3673 , 4229 , 341 , 5003 ) ( 4733 , 4063 , 5197 , 6793 ) ( 11399 , 13969 , 5371 , 16339 ) ( 24761 , 32731 , 1009 , 36901 ) ( 1667 , 1399 , 3541 , 3727 ) ( 1087 , 1661 , 509 , 1817 ) ( 13631 , 21139 , 2521 , 22891 ) ( 1931 , 3697 , 3163 , 4471 ) ( 109 , 437 , 293 , 479 ) ( 2099 , 6883 , 2377 , 7039 ) ( 2603 , 11821 , 319 , 11863 ) ( 55385 , 11437 , 37937 , 60911 ) ( 82037 , 37225 , 36341 , 86699 ) ( 98783 , 53395 , 34211 , 104957 ) ( 141275 , 94447 , 25127 , 154361 ) ( 8167 , 2537 , 5041 , 8833 ) ( 69883 , 30257 , 34669 , 74329 ) ( 102295 , 62093 , 30481 , 110197 ) ( 146899 , 105929 , 19477 , 163441 ) ( 4229 , 341 , 3673 , 5003 ) ( 5311 , 1423 , 3671 , 5869 ) ( 8027 , 4139 , 3547 , 8585 ) ( 9757 , 5869 , 3329 , 10531 ) ( 437 , 293 , 109 , 479 ) ( 14201 , 10313 , 2341 , 15839 ) ( 17011 , 13123 , 1475 , 19297 ) ( 39509 , 8479 , 30743 , 45035 ) ( 3803 , 1429 , 2369 , 4145 ) ( 74843 , 44461 , 29105 , 81017 ) ( 110519 , 80809 , 22133 , 123605 ) ( 10253 , 7999 , 1199 , 11675 ) ( 32203 , 4727 , 28447 , 38377 ) ( 77731 , 51983 , 26119 , 85633 ) ( 94933 , 69857 , 22717 , 106507 ) ( 1241 , 355 , 983 , 1427 ) ( 2435 , 1621 , 941 , 2693 ) ( 4469 , 3775 , 443 , 5231 ) ( 26993 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I had to stop here. Otherwise Quora's mods could ban me because of spam. Don't forget to check every example individually, some of them recur:).

Hamites and Cushites are not Caucasoids. They are Ethiopoid.In addition, Cushites are a category of Hamites. They are not separate categories.Biblical Ham looked like a Somali. It is the only truth. Somali have the highest frequency of the e1b1b hg associated with Hamitic people. The e1b1b hg peaks at 88% amongst Somali populations.Ethiopoids are much much older than the “so-called Caucasoids”. Ethiopians are mentioned in the Bible a hundredfold long before the word Caucasoid (Caucasian like) was coined by German anthropologist Johann Friedrich Blumenbach in the late 18th.Ethiopia - the most extraordinary country in the WorldEthiopia has had effect on much countries in the world whether people know it or not. Apart from being the oldest country in the world with more than 2,500 years of existence (San Marino (Europe's oldest country) is around 1,700 years old), it also has had immense influence on both Christianity, Islam and Rastafarianism. Ethiopias population has reached 100 million people placing them 2nd to Nigeria (200 million) in Africa.10 Oldest Countries in the World - AllTheRooms - The Vacation Rental ExpertsEthiopiaMany historians agree that Ethiopia is one of the oldest countries in the world. While we know that human life has existed in Ethiopia for millions of years thanks to skeletal fragments uncovered, it’s generally agreed that Ethiopia developed as a country in 980 BCE. This was when one of the first kingdoms, known as the D’mt, rose to power. Ethiopia is one of the few African countries that never fell into the hands of colonizers, with the exception of when it was occupied for a few years under Italian dictator Mussolini in the 1930s.Lady Lugard/Flora Shaw Lugard, Asa G. Hilliard, III, A Tropical Dependency: An Outline of the Ancient History of the Western Sudan With an Account of the Modern Settlement of Northern Nigeria, Black Classic Press (1996)"The fame of the ancient Ethiopians (ancient Kushites) was widespread in ancient history. Herodotus described them as the tallest, most beautiful and long-lived of the human races, and before Herodotus, Homer, in even more flattering language, described them as the most just of men, the favorites of the gods. The annals of all the great early nations of Asia Minor full of them. The Mosaic records allude to them frequently; but while they are described as the most powerful, the most just, and the most beautiful of the human race, they are constantly spoken of as Black, and there seems to be no other conclusion to be drawn than at that remote period of history, the leading race of the Western World was a Black race."…..Three quotes from Quora Users for you to ponder.Racism was what made the Eurocentrics classify Ham as all "black" people first (to justify slavery and colonization) then they all magically became "white" people after that point so that they could claim Egypt for themselves.Hamites" cursed as "blacks" now become "white" and therefore the just progenitors of civilization in Africa, beginning with Egypt.The Hamite went from being the cursed father of African people, doomed to slavery, to being some superior, civilizing white or near white race in order to rationalize the presence of civilization in Egypt.Ham (2) Definition and Meaning - Bible DictionaryHam[N] [H] [S]warm, hot, and hence the south; also an Egyptian word meaning "black", the youngest son of Noah ( Genesis 5:32 ; comp Genesis 9:22 Genesis 9:24 ). The curse pronounced by Noah against Ham, properly against Canaan his fourth son, was accomplished when the Jews subsequently exterminated the Canaanites.One of the most important facts recorded in Genesis 10 is the foundation of the earliest monarchy in Babylonia by Nimrod the grandson of Ham (6,8,10). The primitive Babylonian empire was thus Hamitic, and of a cognate race with the primitive inhabitants of Arabia and of Ethiopia. (See ACCAD .)The race of Ham were the most energetic of all the descendants of Noah in the early times of the post-diluvian world.Hidden Africans Of The Bible And Early ChurchBiblical scholars are aware that “Cush” sometimes refers to all of Africa, sometimes to all of Africa except Egypt, and sometimes to ancient Nubia, stretching from modern Aswan in the north to Khartoum in the south. Today most of this area lies in the Sudan.But how is the general reader to understand that Cush and Cushite (used 57 times in the Hebrew Bible) are in fact a designation for an African nation and people? Some versions of the Bible translate “Cush” as “Ethiopia,” but this does not ordinarily designate the modern country of that name. David Adamo has suggested that the best translation is simply “Africa.”Africa In The Old TestamentWe read in Genesis that one of the rivers of Eden ran around the whole land of Cush, and another encircled the land of Havilah that yielded gold and onyx and bdellium (2:10-13). These products were found in antiquity principally in the area now known as the Sudan. If the Tigris and Euphrates rivers are located in Babylonia, then there is good reason to believe some of Eden lay in Africa. We are now told that the oldest human remains may also be traced to Africa.Hagar, the Egyptian concubine of Abraham, may well have derived her ancestry from south of Egypt, and she alone of all the Bible characters gives God a name (Gen 16:13). Like Abraham, she meets God in the form of an angel and is given a promise that her progeny shall become a great nation (Gen 21:18).Moses’ Cushite wife aroused the bitter jealousy of his sister Miriam. (Num 12:11-16). Amusingly, Miriam, who resents her black sister-in-law, becomes white with leprosy until she mends her ways. If this Cushite wife was Zipporah, then the Moses’ father-in-law is Jethro the priest, who instituted the judicial, administrative and sacrificial patterns of Israel (Ex 18:1-27). He and his family had received the exiled Moses during Moses’ forty years as a shepherd in Sinai.Zipporah had understood the importance of circumcision and performed the ritual on their sons (Ex 18:1-27). Even if the Cushite wife refers to a second spouse, then Moses also looks to his new father-in-law for guidance and direction (Num 10:29-32; Jdg 1:16).When the Israelites settle the land of Canaan, there were Africans among them. Some may have left Egypt along with the Israelites at the time of the Exodus; others came with military invaders (1 Kg 14:25-28; 2 Chr 12:2-3; 14:9-15; cf. 16:8). Apparently an Ethiopian colony was created at Gerar as a buffer between Egypt and Judah. Thus, the Ethiopians became permanent residents in Palestine, remaining there until time of Hezekiah (715-685 BCE).Accordingly we read, “They journeyed to the entrance of Gedor, to the east side of the valley, to seek pasture for their flocks, where they found rich, good pasture, and the land was very broad, quiet, and peaceful; for the former inhabitants there belonged to Ham” (1 Chr 4:39-40). Further, a group of Philistines and Arabs were said to be settled “near the Ethiopians” (2 Chr 21:16).Persons of African descent appear to have taken an active role in Israel’s social and political life. The bride in Song of Solomon is “black and beautiful” (Song 1:5). A Cushite who possessed tact, discretion, and a high position in the royal court appeared as a trusted courtier sent to tell David news of Absalom’s death (2 Sam 18:19-32).Africans continued to enjoy royal favor, as Solomon married an Egyptian princess (1 Kg 9:16, 24; 2 Chr 8:11) and received the Queen of Sheba (1 Kg 10:1-13; 2 Chr 9:1-2). This influential queen ruled dark-skinned peoples on both sides of the Red Sea, and she may well have initially come to Solomon to negotiate a trade treaty with his growing maritime power. Though she tested him with hard questions, in the end she told him all that was in her heart. It appears that in this black woman Solomon found a kindred spirit with whom he could discourse freely.Whether or not that relationship was sexual, there is evidence that other alliances did indeed produce children. Zephaniah, a descendant of Hezekiah, is called the son of Cushi and brings special prophecies about Cush (Zeph 1:1; 3:10). Jehudi, the courtier sent to bear Jeremiah’s message from Baruch to King Zedekiah, appears to have had a Cushite ancestor (Jer 36:14). Faithfully, Baruch stands before the king, reading the words of God, while the king slashes the scroll and casts it in the fire (Jer 36: 21, 23).Ebed-Melek, a confidential advisor of the king, is identified as a Cushite four times (Jer 38:7, 10, 12; 39:16). Believing that Jeremiah was bringing God’s authentic voice to Judah, Ebed-Melek risked his life to rescue the prophet from the cistern and secure for him a hearing with the king. Jeremiah commends the courtier’s faith (39:15-18) and proclaims to him a special covenant of God’s protection.When Cushite pharaohs ruled over Egypt, they contracted military alliances with both Israel and Judah, especially during the time of the Twenty-fifth or Cushite Dynasty. Sabacho (716-701 BC, called So in 2 Kings 17:4) contracted an alliance against Assyria with Hoshea, king of Israel, while Tirhakah (690-664) came to the aid of Hezekiah when Jerusalem was beseiged (2 Kg 19:9; Is 37:9). Mortuary figurines of Tirhakah clearly reveal his African features, and his enormous statue still towers above the great temple complex at Karnak.Africa In The New TestamentThe kingdom of Cush continues to play a role in the New Testament, where we read of the conversion of Candace’s Ethiopian treasurer (Acts 8:26-39). Candace was the royal title of the Queen Mother of Nubia, a powerful African nation located principally in what is now Sudan. Greek was spoken in the court, so the chamberlain would have had no problem reading a Septuagint version of the prophet Isaiah; and Philip, a Greek-speaking Jew, would easily have communicated the Gospel to him.It was Candace who wielded the real political and military power from her capitol city in Meroe while her son served as a religious figurehead. The royal mother made gifts to deities on behalf of the kingdom and may have sent her chamberlain with a gift to Jerusalem. The arts of civilization flourished at a high level throughout her realm, and twice her forces engaged the Roman army in battle.Further to the north lay Cyrene, capital city of the Roman province Cyrenaica. The city was famous for three schools of philosophy and for native sons who excelled in medicine, mathematics, rhetoric and literature. Perhaps the most illustrious of these was the astronomer Eratosthenes, who in approximately 200 BC computed the circumference of the earth with remarkable accuracy. No less brilliant was the Hellenistic poet Callimachus, who became the director of the library at Alexandria and acquired an astonishing reputation for the versatility of his aptitudes. Athletes from Cyrene excelled in Olympic competition, especially in horse chariot racing.Ships carried corn, oil and wool from the fertile fields of Cyrene, as well as a contraceptive known as sylphium, much sought after in Rome. Cyrene maintained a monopoly on the herb until it became extinct through overharvesting approximately AD 200.The citizens of Cyrene roamed far and wide throughout the Mediterannean world as merchants, athletes, philosophers, orators, mercenaries and entertainers. The Jewish community of the city had a deep interest in Judaism and produced an important literature including a five-book history of the Maccabees by Jason the Cyrenian (2 Maccabees 2:43). There were close ties with Jerusalem. Simon of Cyrene may have been impressed to carry the cross of Jesus when he came as a devout Jew to pay a Passover visit to Jerusalem. Apparently he became a believer, and his sons were known to the Christian community (Mk 15:21; cf. Rom 16:13).Although an African synagogue, that of the Cyreneans and Alexandrians, first objected to the preaching of Stephen (Acts 6:9), other natives of Cyrene became early adherents of Christianity and carried the good news to Cyprus (Acts 11:19-26). From there Cyrenians and Cyprians travelled on to Antioch and innovated a Gospel approach to non-Jewish Greeks. This revolutionary action drew the attention of the Jerusalem Council, and Barnabas was dispatched to assess this new development. Convinced of the authenticity of the mission, Barnabas strategized with the leaders and went to Tarsus to seek out Paul. Implementation of the Africans’ dream would require the involvement of a multinational and multicultural task force. As the church at Antioch prayed, searched the Scriptures and strategized for a full year, a core of leaders developed. Of the five who are named, two are African: Lucius of Cyrene, and Simon called the Black (Acts 13:1-2). Here again, translations fail to inform us that “Niger” is Latin for “Black.” This may well be none other than Simon of Cyrene.The missionary agency was in large part initiated, strategized, promoted and directed by Africans. The story of Acts tells us that Paul and Barnabas were promptly sent to Cyprus, home of some members of the Antiochene community (Acts 13:4-12), but archaeological evidence tells us of the arrival of the Gospel in Cyrene. By the end of the first century AD, there were Christian burials inside the Jewish cemetery at Cyrene.Africans In The Early ChurchClement of Alexandria (150-215) was a Christian philosopher with a keen desire to win pagan intellectuals to Christ. He directed a catechetical school at Alexandria and wrote important exhortations to the heathen as well as to Christians, calling them to a more perfect life in Christ. Another African, Origen (185-254), became the director of a catechetical school at age 18. His was the finest mind the church would produce in 300 years. Origen was highly successful in debating Jews, pagans, and Gnostics, and is in fact credited with destroying Gnosticism. This important biblical scholar, theologian, exegete, and pioneer in biblical criticism produced the Hexapla, comparing six versions of the Bible. He profoundly influenced the theological thought of the succeeding centuries.Tertullian (160-225) was a pagan lawyer who converted to Christianity. He authored apologetic, theological, and controversial works, and was the first theologian to write in Latin. It was he who formulated the doctrine of the Trinity, and coined nearly a thousand new words to explain Christian truths.Athanasius (296-373), was Bishop of Alexandria and a major theologian and writer. He was the chief upholder of the doctrine that Christ was both man and God, and was the principle opponent of the Arian doctrine that Jesus was man rather than God. Even as a very young deacon, he was influential at the Council of Nicea. Opponents referred to him as the “black dwarf.” He was repeatedly exiled and persecuted, but his principles ultimately prevailed at the Council of Constantinople in 381.Cyril, who died in 444, was also Bishop of Alexandria. He brilliantly represented and systematized the teachings of Athanasius and other Alexandrians. He was a vigorous opponent of heresy.Perpetua and Felicitas were two martyrs who died in the Carthage arena in 202. Their story was widely used in winning others to Christ.Cyprian, Bishop of Carthage, died a martyr in 258. He possessed a profound knowledge of Scriptures, wrote important theological works, fought heresy, and insisted on the unity of the Church.Lactantius (c. AD 317) is best known for his Institutes, described as the “most comprehensive apology which Christianity created before the end of the time of persecution.” The major theme of the Institutes is justice. Lactantius insisted that God had given humanity a way of life open to all people regardless of race, education, sex, color or creed.St. Maurice of Aganum (born about 287) was a Roman general who refused to kill Christians during the slave revolt in Gaul. He declared to the emperor Maximian:We cannot obey you without denying God, the Creator of all things, our Master as well as yours, whether you acknowledge it or not.He was slaughtered by imperial decree along with his regiment for his defense of slaves.G. Marius Victorinus (280-363) was a neoplatonist professor of rhetoric with a brilliant record as philosopher and scholar. Educated in Africa but taught in Rome, he wrote theological and devotional works that were to lead to the conversion of Augustine.Augustine (354-430), Bishop of Hippo, was one of the Doctors of the Church. A profoundly influential theologian, he dealt with three heresies: Manichaeism, Donatism, and Pelagianism. Augustine had remarkable insights into the human heart and soul. His most famous work is Confessions, written to describe his conversion and win others to Christ by detailing the philosophical basis for Christianity. Monica (331-387) was Augustine’s prayerful and powerful mother.Zeno of Verona served as bishop of Verona from 362 to 375. Over one hundred of his tractates survive as well as a collection of sermons.Optatus of Melevis served as a Bishop in North Africa. He worked to reconcile Christians during the Donatist Schism, and was influential in the East and West as well as in Africa. He died before 400 AD.By 480 Victor of Vita served as Bishop in the province of Byzacena. He described the survival of the Church during an invasion of vandals. He perceived that the persecution was not only religious but also political.Bishop Vigilius of Thapsus participated in a religious synod between the Arians and the Orthodox in 484. He produced important theological and ecclesiastical works.Fulgentius of Ruspe (467-533) was a Roman civil servant who resigned his post to enter the priesthood. In 507 he was elected bishop of Ruspe. Later driven out of Africa by the Vandals, he was instrumental in popularizing Augustine’s work.Three early popes were African. Pope Victor I (AD 189-199) popularized Latin as the common language of the church, thereby making Christianity more democratic and accessible to ordinary people. Pope Melchaides (311-314, sometimes known as Meltiades) was persecuted prior to his reign as pope. He was considered one of the African Christian martyrs. Pope Gelasius I (A.D. 492-496) worked to settle conflicts in church and believed that “both civil and sacred powers are of divine origin, and independent, each in its own sphere.”