When 2²⁵⁶ is divided by 17, the remainder would be :

A. 1

B. 14

C. 16

D. None of these

Answer: Option A

Solution(By Examveda Team)

When n is even, (xⁿ - aⁿ) is divisible by (x + a)
Now, 2²⁵⁶ = (2⁴)⁶⁴ = (16)⁶⁴
∴ (16⁶⁴ - 1⁶⁴) is divisible by (16 + 1)
⇒ (16⁶⁴ - 1) is divisible by 17
⇒ (2²⁵⁶ - 1) is divisible by 17
⇒ On dividing 2²⁵⁶ by 17, we get 1 as remainder.