Prove that `x^n-y^n` is divisible by x - y for all positive integers n.

Answer

which is divisble by a-b . This implies tht P(K+1) is true. The validity of P(K+1) follows from that of P(k).Therefore by the principle of mathematical induction. `a^(n)-b^(n)` is divisible by a-b , where a > b, for all natural numbers n.