If a and b are distinct integers, prove that a – b is a factor of an – InterviewSolution

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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]

Answer»

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]

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