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Source: Irish Mathematics Olympiad 1992 Paper 2 Q1

November 7, 2015
algebra

Problem Statement

Let n>2n > 2 be an integer and let m=∑k3m = \sum k^3, where the sum is taken over all integers kk with 1≤k<n1 \leq k < n that are relatively prime to nn. Prove that nn divides mm.
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