TITLE: How to prove that for all $m,n\in\mathbb N$, $\ 56786730 \mid mn(m^{60}-n^{60})$?
QUESTION [7 upvotes]: How to prove $\forall m,n\in\mathbb N$:
$$ 56786730 \mid mn(m^{60}-n^{60})?$$
Thanks in advance.

REPLY [4 votes]: Hint $\ $ Apply little Fermat, noticing that $\rm\displaystyle\ 56786730\ = \!\!\prod_{\large {\begin{array}\rm p\ prime\\ \rm p-1\mid\, 60\end{array}}}\! p$