# $\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$

how to prove : $\forall m,n \in \Bbb N$ : $$56786730\mid mn(m^{60}-n^{60})$$

my effort:

$56786730=2.3.5.7.11.13.1841$ -Is $1841$ prime?

we must be prove: $2|m n(m^{60}-n^{60})$,...,$13|mn(m^{60}-n^{60})$ but how?

by using Fermat theorem we have if $\gcd(m,i)=1 , \gcd(n,i)=1 , (n)m^{i-1} \equiv 1 \pmod i, i=2,3,5,7,11,13$so $2|mn(m^{60}-n^{60})$,...,$13|mn(m^{60}-n^{60})$ because $i|0, i=2,3,5,7,11,13$ and $1,2,4,6,10,12$ divide $60$

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