APMO 2014 Problem 3

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Answer

Find all positive integers $n$ such that for any integer $k$ there exists an integer $a$ for which $a^{3}+a-k$ is divisible by $n$ . (Warut Suksompong, Thailand)

Dataset text NuminaMath olympiads. Quoted with source.

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All integers $n=3^{b}$ , where $b$ is a nonnegative integer.

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