What is the remainder when 2³¹ is divided by 5 ?

A. 1

B. 2

C. 3

D. 4

Answer: Option C

Solution(By Examveda Team)

2³¹
= 2 × 2³⁰
= 2 × (2² )¹⁵
= 2 × 4¹⁵
When n is odd, (xⁿ + aⁿ) is divisible by (x + a)
∴ (4¹⁵ + 1¹⁵) is divisible by (4 + 1)
⇒ (4¹⁵ + 1) is divisible by 5
⇒ (2³⁰ + 1) is divisible by 5
⇒ On dividing 2³⁰ by 5, we get (5 - 1) i.e., 4 as remainder.
∴ Remainder obtained on dividing 2³¹ by 5
= Remainder obtained in dividing (2 × 4) i.e., 8 by 5 = 3