First slide

Introduction to P.M.I

Question

The remainder when 5⁹⁹ bee is divided by 13, is

Easy

A

6
B

8
C

9
D

10

Solution

$\begin{matrix} 5^{99} = 5 {(5^{2})}^{49} = 5 (25)^{49} = 5 (26 - 1)^{49} \\ = 5 \times 26 \times (positive term) - 5 \end{matrix}$
So, when it is divided by 13, it gives the remainder - 5 or 8

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