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Exist big m such that...

Source: Serbia Math Olympiad 2016 P1

April 1, 2016
number theorySerbiaDivisibility

Problem Statement

Let n>1n>1 be an integer. Prove that there exist m>nnm>n^n such that nm−mnm+n\frac {n^m-m^n}{m+n} is a positive integer.
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