Prove For any natural number n, x^n – y^n is divisible by x – y, where x integers with x ≠ y.

As indicated by the inquiry,

   

is detachable by

   

whole numbers with

   

.

In this way, subbing various qualities for n, we get,

   

Which is separable by

   

   

Which is separable by

   

   

   

Which is separable by

   

   

   

Which is separable by

   

Let

   

be separable by

   

Thus, we get,

   

Presently, we additionally get that,

   

   

   

Which is separable by

   

   

is valid when P(k) is valid.

Along these lines, by Mathematical Induction,

   

is distinct by

   

where x numbers with x ≠ y which is valid for any normal number n.