(9⁶ + 1) when divided by 8, would leave a remainder of :

A. 0

B. 1

C. 2

D. 3

Answer: Option C

Solution(By Examveda Team)

(xⁿ - aⁿ) is divisible by (x - a) for all values of n
∴ (9⁶ - 1⁶) is divisible by (9 - 1)
⇒ (9⁶ - 1) is divisible by 8
⇒ on dividing (9⁶ + 1) by 8, we get 2 as remainder.