Question

If $n$ is an even positive integer, then $a^n+b^n$ is divisible by

• A. $a+b$
• B. $a-b$
• C. $a^2-b^2$
• D. none of these

Answer 1

The correct option is D none of these

Expression is $a^n+b^n$

The expression is never divisible by $(a-b)$.

When n is odd, it is divisible by$(a+b)$.

When n is even it is not divisible by $(a+b)$

So, it is not divisible by $(a-b)(a+b)=a^2-b^2$, when $n$ is even.

The correct answer is option D.