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Can someone provide hints on the following? I am supposed to show that

x^n - y^n is divisible by (x-y), where x and y are integers and y < x.

I got to where I would need to show that

x^(n+1) - y^(n+1) = some K*(x-y).

But I am not sure what to do next?

By brute force I think the division would need to be in the form of x^n + yx^(n-1) ... + y^(n-1)

but how would I show something like that?

Thanks!!