Chapter 8.4, Problem 11ES

In 9-11, prove each of the given statements, assuming that $a,b,c,d,$and n are integers with n>1 and that $a=c\left(\mathrm{mod}n\right)$and $b=d\left(\mathrm{mod}n\right)$.

$a^{nc}=c^{ns}\left(\mathrm{mod}n\right)$ for every integer $m\ge 1$ (Use mathematical induction on m.)