Question

When $3^{37}$ is divided by $80$ , the remainder is

• A. 3
• B. 4
• C. 6
• D. none of these

Answer 1

Answer: (A)

We have, $3^{37}=3^{4.9}\cdot 3=3(81{)}^9=3(80+1{)}^9$
$=3\left({}^9{C}_0\cdot 80^9+{}^9{C}_{1}80^8+\dots +{}^9{C}_9\right)$
Thus, when $3^{37}$ is divided by $80$ , the $m$ remainder is $3$ .