For integer $n\ge2$, Is there always a prime p such that $v_p(n^3-n)=1$?
For example,
$n=2$: $p=2$ $(6=2\times3)$
$n=3$: $p=3$ $(24=2^3\times3)$
$n=9$: $p=5$ $(720=2^4\times 3^2\times5)$
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prove that there is a prime p such that $v_p(n^3-n)=1$
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