If A And B Are Distinct Integers, Prove That A – B Is a Factor Of An – Bn, Whenever N Is a Positive Integer. - CBSE (Arts) Class 11 - Mathematics
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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]
In order to prove that (a – b) is a factor of (an – bn), it has to be proved that
an – bn = k (a – b), where k is some natural number
It can be written that, a = a – b + b
Is there an error in this question or solution?
Solution If A And B Are Distinct Integers, Prove That A – B Is a Factor Of An – Bn, Whenever N Is a Positive Integer. Concept: Binomial Theorem for Positive Integral Indices.