Question

Find the remainder when `5^(99)` is divided by 13.
A. 6
B. 8
C. 9
D. 10

Answer 1

Correct Answer - B

Answer 2

5⁹⁹ = 5.5⁹⁸ = 5(5²)⁴⁹ = 5(26-1)⁴⁹

--> apply binomial expansion for the bracket then you will get 

5(26K-1) where k is an integer,

Now, divide by 13 

5(26K)/13-5/13 

-5 is the remainder but remainder can't be negative so answer will be -5 + 13 = +8.