# If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer. [Hint write an = (a – b + b)n and expand]

We can write an as

an = (a-b+b)n

We know that-

putting a = b & b = a-b, we get-

where

Hence (a-b) is a factor of (an-bn).

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