Let $n$ be an integer not divisible by $3$. Show that $n^7 ≡ n (\mod 63)$.
I know that we can split $63$ into $3^2 \cdot 7$ So we have $n^7=n (\mod 7\cdot3^2)$
$n^7=n (\mod 3^2)$ and $n^7 = n (\mod 7)$
And I am stuck how to go about solving this question after this