# 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.

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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.

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Solution:

To prove that ( a – b ) is a factor of ( a n – b n ), we have to first proved that

a n – b n k ( a – b ), where k is some natural number

It can be written that, a = a – b + b

This shows that ( a – b ) is a factor of ( a n – b n ), where n is a positive integer.