Question

If $x$ and $y$ are two distinct integers and $n$ is a natural number then $x^n-y^n$ is divisible by

• A. $x^2-y^2$
• B. $x+y$
• C. $x-y$
• D. None of these

Answer 1

Answer: (C)

$P\left(n\right):x^n-y^n$ where $n\in N$
Then, $P\left(1\right):x-y$ is divisible $x-y$
$P\left(2\right):x^2-y^2$ is divisible $x-y$
$P\left(3\right):x^3-y^3$ is divisible $x-y$
Hence $x^n-y^n$ is divisible $x-y$