1a) Find all integers >1 for which n^4+4^n is a prime.
b) Show that 1001| (1^1993+2^1993+...+1000^1993)
c) 2903^n-803^n-464^n+261^n is divisible by 1897 for all natural numbers n.
2) Find the remained when the sum 1+2+3...+100 is divided by 4.
3) Find the remained der when 1+2!+3!...+100! is divided by 12.
4) Are there any integers x and y such that x^2-5y^2=2?
b) How many integers are there such that n such that 2^n+27 is divisible by 7?
5) Is it true that every year including any leap year, has at least one Friday 13th? Justify your answer.
2006-08-14
00:56:22
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4 answers
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asked by
edwinvandesar
1
in
Mathematics