Question

The least remainder when $17^{30}$ is divided by $5$ , is

• A. 2
• B. 1
• C. 4
• D. 3

Answer 1

Answer: (C)

$(17{)}^2=289\equiv (-1)(\mathrm{mod}5)$
$\Rightarrow {\left(17^2\right)}^{15}\equiv (-1{)}^{15}(\mathrm{mod}5)$
$\Rightarrow 17^{30}\equiv -(\mathrm{mod}5)$
i.e., $17^{30}\equiv 4(\mathrm{mod}5)$