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Divisibility related to powers

Source: Canadian Mathematical Olympiad - 1986 - Problem 4.

July 3, 2011

number theory unsolvednumber theory

Problem Statement

For all positive integers

n

and

k

, define

F(n,k) = \sum_{r = 1}^n r^{2k - 1}

. Prove that

F(n,1)

divides

F(n,k)