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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Induction

NTA Abhyas 2020 · Mathematics · Mathematical Induction

If x and y are two distinct integers and n is a natural number then...

If

x

and

y

are two distinct integers and

n

is a natural number then

x^{n} - y^{n}

is divisible by

Options

A $x^{2} - y^{2}$
B $x + y$
C $x - y$
DNone of these

Correct answer

C. $x - y$

Step-by-step solution

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

where

n \in \mathbb{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

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