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  4. If x and y are two distinct integers and n is a natural number then xn-yn is divisible by

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

NTA AbhyasNTA Abhyas 2020Principle of Mathematical Induction

Solution:

$P\left(n\right):x^{n}-y^{n}$ 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 $x-y$