Question

If $a,b$ are distinct rational numbers, then for all $n\in N$ the number $a^n-b^n$ is divisible by

• A. $a-b$
• B. $a+b$
• C. $2a-b$
• D. $a-2b$

Answer 1

The correct option is A $a-b$

We know, $a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}{b}^2+.......+a^2{b}^{n3}+a{b}^{n2}+b^{n1})$
Hence $(a-b)$ is one of its factor.