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p divides 1^n + 2^n +... + (p + 1)^n.

Source: 2014 Saudi Arabia GMO TST II p2

July 26, 2020
Sum of powersnumber theorydividesdivisible

Problem Statement

Let pp be a prime number. Prove that there exist infinitely many positive integers nn such that pp divides 1n+2n+...+(p+1)n.1^n + 2^n +... + (p + 1)^n.
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