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PDF Editor FAQ

If a, b, c and d are prime integers such that 1<a<b<c<d and abcd=1430, then what is the value of d?

The product of abcd is an even number. Hence 2 must definitely be there. If a= 2 only, we can get the product as even number. Hence the product of bcd is 715. The factors of 715 are 5,11 and 13. Therefore b=5, c=11 and d=13.

51b2cd is a six digit perfect square that is divisible by both 5 and 11. What is the sum of all possible values of it?

For the number 51b2cd to be divisible by 5 and 11, the number d should be 0 or 5. For any number to be divisible by 11 the difference between the sum of the digits at odd places should be as the sum of the digits at even places.Thus, if d = 5, then 5+b+c = 1+2+5 or b+c = 35+b+c = 1+2+0 = 3 or b+c = -2. Add 11 to the sum to get 9 as = b+c.If b = 1, c = 2. So, the number is 511225. But it is a perfect square or 715, so it is a solution.Hence there is only one number: 511225 which is divisible by 5 and 11 and is a square of 715. The sum of, b, c and c = 1+2+5 = 8.

What were relations like between ancient Egyptians and the rest of Africa?

It depends on the period of Ancient Egypt’s long History, but, generally:Libya was considered an enemy, Libyans conquered areas of the Delta and set a dynasty, the XXIII, from 818 to 715 b. C.Sudan (Kush) also called lower Ethiopia, was believed to be one of the origins of the Egyptian Civilization, sometimes it was an ally, other times was considered enemy, and other times was a tributary region. Kushites conquered Egypt at the time of the Libyan invasion and set the XXV ruling dynasty (747-644 b. C.) controlling all Egypt, all northern Sudan (Kush), some parts of Libya and some parts of the Asian Mediterranean Coast.Somalia (Punt), and harbours in the Red Sea were considered good trading points with friendship relations with Egypt.Other areas where vaguely known for instance the areas where the pigmy people came from. Maybe these areas are today located in the Central African Republic. It is believed that the god Bes represents a pigmy. Bes was a protective deity.Some traditionalist believe Egyptians, as a people, had their origins in present Chad, a land considered for them sacred or mythical (the land of the fading sun).Generally Egyptians, like many Ancient peoples, where very ethnocentric, xenophobic and reluctant to any foreign influence, in Africa or outside Africa.

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