Q. The remainder when $5^{99}$ is divided by 13, is
A) 6
B) 8
C) 9
D) 10
Explanation
(b)
$5^{99} = 5\left( 5^{2} \right)^{49} = 5(25)^{49}$
$= 5(26 - 1)^{49}$
$= 5 \times 26 \times (Positive\ term) - 5$
So, when it is divided by 13, it gives the remainder $- 5$ or 8.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.