Let $a$ and $b$ be different positive rational numbers such that the there exist an infinity of positive integers $n$ for which $a^n - b^n$ is an integer. Prove that $a$ and $b$ are also integers.
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Tags: number theory, 3rd edition
Let $a$ and $b$ be different positive rational numbers such that the there exist an infinity of positive integers $n$ for which $a^n - b^n$ is an integer. Prove that $a$ and $b$ are also integers.