Question

What will be the remainder if $2^{100}$ is divided by $17$ ?

Answer 1

$\frac{2^{100}}{17}=\frac{(2^4{)}^{25}}{16+1}=\frac{(16{)}^{25}}{16+1}$

acc to Remainder Theorem : $[\frac{(a+1{)}^n}{a}=1]$

so, $\frac{(16{)}^{25}}{16+1}=1$

$\therefore$ Remainder = 1