Question

prove that X^n - Y^n is divisible by (x-y)​

Answer 1

Answer:

Let P(n) : xn – yn is divisible by x – y, where x and y are any integers with x≠y. Let us assume that, P(n) is true for some natural number n = k. Now, we have to prove that P(k + 1) is true. Hence, P(k + 1) is true whenever P(k) is true.