Question

The number with which ${23}^n-1$ is divisble by :

• A. $5$
• B. $7$
• C. $9$
• D. $11$

Answer 1

Answer: (D)

$11$

$a^n-b^n$ is divisible by $a-b$ (By Factor Theorem)
Hence, ${23}^n-1={23}^n-1^n$ is divisible by $23-1=22$
So, it is divisible by $11$.