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Q.
When $3^{37}$ is divided by $80$ , the remainder is
Binomial Theorem
Solution:
We have, $3^{37}=3^{4.9} \cdot 3=3(81)^{9}=3(80+1)^{9}$
$=3\left({ }^{9} C_{0} \cdot 80^{9}+{ }^{9} C_{1} 80^{8}+\ldots+{ }^{9} C_{9}\right)$
Thus, when $3^{37}$ is divided by $80$ , the $m$ remainder is $3$ .