Question

When $2^{301}$ is divided by $5$, the least positive remainder is

Answer 1

Answer: 2

$2^4\equiv 1$(mod $5$) ;
$\Rightarrow (2^4{)}^{75}\equiv (1{)}^{75}$ (mod $5)$
i.e., $2^{300}\equiv 1$(mod $5$)
$\Rightarrow 2^{300}\times 2\equiv (1\times 2)$( mod $5$)
$\Rightarrow 2^{301}\equiv 2($ mod $5$)
$\therefore$ Least positive remainder is $2$.