If and are distinct integers

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

1. If

a

and

b

are distinct integers, prove that

a-b

is a factor of

a^{n}-b^{n}

, whenever

n

is a positive integer. [Hint write

a^{n}=(a-b+b)^{n}

and expand]

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