KöMaL problem A, 2019

Number theory Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Let $c>0$ be a real number, and suppose that for every positive integer $n$ , at least one percent of the numbers $1^c,2^c,3^c,\ldots,n^c$ are integers. Prove that $c$ is an integer.

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