First slide

Binomial theorem for positive integral Index

Question

When 3³⁷ is divided by 80, the remainder is

Moderate

A

3
B

4
C

6
D

none of these

Solution

We have,
$3^{37} = 3^{4 .9} \cdot 3 = 3 (81)^{9} = 3 (80 + 1)^{9}$
$= 3 (^{9} C_{0} \cdot 80^{9} +^{9} C_{1} 80^{8} + \dots +^{9} C_{9})$
Thus, when 3³⁷ is divided by 80, then the remainder is 3.

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