The remainder left when $8^{2 n}-(62)^{2 n+1}$ is divided by 9 is

Question

Professor PC Thomas Classes · Answer

$8^{2n} \equiv (-1)^{2n} \equiv 1 \pmod 9$. $62 \equiv -1 \pmod 9 \implies 62^{2n+1} \equiv -1 \pmod 9$. $1 - (-1) = 2$.