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When Kanye West, in Black Skinhead, states “ I keep it 300, like the Romans,” what historical event involving 300 Romans is he referring to?
It is safe to say that Kanye West is not a classicist some pick it up as the 300 Spartans in Thermopalye though others may go to the incident mentioned by the historian Livy that in 358 BC, Rome declared war on Tarquinii after forces from that city had raided Roman territory. Consul Gaius Fabius Ambustus was assigned to that war. However, the Tarquinienses defeated Fabius and sacrificed 307 Roman prisoners of war. Howwever, I suspect he is trying to be terribly clever on Rap Genius an apologist has already explained this away as “Also, the Roman Numerals for 300 are CCC, an initial-ism for Calm Cool and Collected — Commonly mistaken for a film-mix up this is actually one of the most genius lyrics ‘Ye has written. To one who is not attentive to Kanye’s lyrical intricacies, this may seem like a mistake. But Kanye is really just ‘cool, calm, and collected’ no matter what — he’s always a few steps ahead of the common man. A real Jesus figure.” Which I think can safely considered to be total bollocks as looking at the lyrics in the chorus goes like this which I got from Genius.com.Four in the mornin', and I'm zonin'They say I'm possessed, it's an omenI keep it 300, like the Romans 300 bitches, where the Trojans?Baby, we livin' in the moment I've been a menace for the longest But I ain't finished, I'm devoted And you know it, and you know itIt has more to to do with it rhyming more than anything else and it does look like he has a book with words that rhyme with each other - the next line 300 bitches, where the Trojans might have to do with the brand of condoms than the Ancient Trojan people the Romans claimed they were descended from but then there was also claims they descended from Greek colonists and the son of Odysseus & Circe called Romos. Basically Kanye West with a side order of the casual misogyny that critics of rap accuse the genre of having just thought that no one would really analyse his lyrics as it is just him mumbling to someone else’s music.
Can the sets of digits of n and n^3 in base 10 be equal and consisting of just four distinct digits? Can the sets of digits of n and n^3 in base 14 be equal and consisting of just five distinct digits?
If I had to bet, I'd say yes, but the fact is that there are no solutions to both questions up to a large limit. For the first question, the limit is 2*10^8. The second question has no solutions up to tetradecimal 12000000. Conjecture: There are solutions to both questions up to H_4(2,6) digits in that bases, where H is the hyperoperation.Note that 24D(0^^n)^3=D02420D(0^^3*n) in base 14. For positive n, the sets of digits of n and n^3 in base 14 are equal and consisting of exactly four different digits. Note also that 16564(0^^n)^3=4544600014144(0^^3*n) in base 10. For positive n, the sets of digits of n and n^3 in base 10 are equal and consisting of exactly five distinct digits. These are only near-misses, not the answers to both questions.If we change the exponent 3 to 2, we have infinitely many solutions:Base 10: 4762^2=22676644, the smallest, or much larger 50025515^2=2502552151015225.Base 14: 13507^2=177505037, or slightly larger A0C37^2=7337AA0C37, or slightly larger 1C3701^2=3730C737001.There are few such results with only four different digits. The only known ones are of the form 461*14^n, nEN.For squares and at most four digits in concatenation of n and n^2 up to tetradecimal 2000000 there are such results, n nonnegative, using Magma.Input:b:=14; [[IntegerToString(n,b),IntegerToString(n^2,b)]: n in [0..2*b^6] | #Set(Intseq(n,b)) le 4 and #Set(Intseq(n,b) cat Intseq(n^2,b)) le 4];Output:[[ 0, 0 ],[ 1, 1 ],[ 2, 4 ],[ 3, 9 ],[ 4, 12 ],[ 5, 1B ],[ 6, 28 ],[ 7, 37 ],[ 8, 48 ],[ 9, 5B ],[ A, 72 ],[ B, 89 ],[ C, A4 ],[ D, C1 ],[ 10, 100 ],[ 11, 121 ],[ 12, 144 ],[ 13, 169 ],[ 14, 192 ],[ 15, 1BB ],[ 17, 237 ],[ 18, 268 ],[ 19, 29B ],[ 1A, 2D2 ],[ 1D, 3A1 ],[ 20, 400 ],[ 21, 441 ],[ 22, 484 ],[ 24, 532 ],[ 25, 57B ],[ 27, 637 ],[ 28, 688 ],[ 2A, 752 ],[ 2C, 824 ],[ 2D, 881 ],[ 30, 900 ],[ 31, 961 ],[ 33, A49 ],[ 35, B3B ],[ 37, C37 ],[ 38, CA8 ],[ 39, D3B ],[ 3D, 1161 ],[ 40, 1200 ],[ 41, 1281 ],[ 42, 1324 ],[ 44, 1452 ],[ 4D, 1A41 ],[ 50, 1B00 ],[ 51, 1BA1 ],[ 57, 2237 ],[ 60, 2800 ],[ 67, 3037 ],[ 70, 3700 ],[ 77, 4037 ],[ 78, 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1101000, 1212201000000 ],[ 1101001, 1212203202001 ],[ 1101010, 1212223020100 ],[ 1101011, 1212225222121 ],[ 1101100, 1212421210000 ],[ 1102000, 1214404000000 ],[ 1110000, 1232100000000 ],[ 1110001, 1232102220001 ],[ 1110010, 1232122200100 ],[ 1110100, 1232322010000 ],[ 1200000, 1440000000000 ],[ 1200001, 1440002400001 ],[ 1200010, 1440024000100 ],[ 1200100, 1440240010000 ],[ 1200101, 1440242410201 ],[ 1201000, 1442401000000 ],[ 1500000, 1BB0000000000 ],[ 2000000, 4000000000000 ]]Note the bouncing phenomenon in the list above.
Comments from Our Customers
It is easy to program and it helped us in automating our quoting system with a fast and easy online app
Justin Miller
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