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=2×3) n=3: p=3 (24=2³×3) n=9: p=5 (720=2⁴×3²×5)
prove that there is a prime p such that $v_p(n^3-n)=1$
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