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1. Find the remainder when 54¹²⁴ is divided by 17.

A. 8

B. 13

C. 16

D. 9

Solution:

\begin{aligned} \frac{54^{124}}{17} \\ O r, \frac{{(17 \times 3 + 3)}^{124}}{17} \\ The remainder would be same as, \\ \frac{3^{124}}{17} \\ O r, \frac{3^{4 \times 31}}{17} \\ Remainder will be same as, \\ \frac{3^{4}}{17} \\ O r, \frac{81}{17} \\ Remainder = 13 \end{aligned}

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