The number (2⁴⁸ - 1) is exactly divisible by two numbers between 60 and 70. The numbers are :

A. 63 and 65

B. 63 and 67

C. 61 and 65

D. 65 and 67

Answer: Option A

Solution(By Examveda Team)

(2⁴⁸ - 1)
= [(2⁶)⁸ - 1]
= (64)⁸ - 1
When n is even , (xⁿ - aⁿ) is completely divisible by both (x - a) and (x + a)
∴ (64⁸ - 1⁸) is divisible by both (64 - 1) and (64 + 1)
⇒ (2⁴⁸ - 1) is divisible by both 63 and 65