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sum from k=1 to (n-1)^p, of k^m

Source: Nordic Mathematical Contest 1990 #1

October 5, 2017
number theorySum of powers

Problem Statement

Let m,n,m, n, and pp be odd positive integers. Prove that the number ∑k=1(n−1)pkm\sum\limits_{k=1}^{{{(n-1)}^{p}}}{{{k}^{m}}} is divisible by nn
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