What is the remainder when $3^{65}$ is divided by 28?

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Solution

The correct option is C 19
$\frac{3^{65}}{28} = \frac{3^{2} (3^{3})^{21}}{28} = \frac{9 (27)^{21}}{28}$
$= 9 \times (28 - 1)^{21} = 9 \times (- 1) = - 9$
Now, Remainder = - 9 + 28 = 19

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