Question

Remainder when $7^{636}$ is divided by 19 is equal to

Answer 1

$7^{636}=(343{)}^{212}=(1+19\times 18{)}^{212}$
$=1{+}^{212}{C}_1(19\times 18){+}^{212}{C}_2(19\times 18{)}^2+.......$
$\Rightarrow$ Remainder $=1$