1)Let p be an odd prime and n a positive integer. In the coordinate plane, eight distinct points with integer coordinates lie on a circle with diameter of length p^n. Prove that there exists a triangle with vertices at three of the given points such that the squares of its side lengths are  integers  divisible by p^n+1

2)Show that 1+2+3+........+n divides 1^k+2^k+...........+n^k, for and odd positive integer k and for nay natural number n

 3)Denote by a, b, c the lengths of the sides of a tria...
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