Question

Find out the remainder when $7^{84}$ is divided by $2402$

Answer 1

use modulo $2402$

$7^{84}$

$\equiv (7^4{)}^{21}$

$\equiv (2401{)}^{21}$

$\equiv (-1{)}^{21}$

$\equiv -1$

$\equiv 2401\left(mod2402\right)$