Hey guys i'm looking to prove that if then we are sure that either either is true, where a,b,N are all positive integers.

And using that (i suppose, but not necessarily), to create an algorithm that given an integer can verify whether it's a power (i mean it can be written in the form).

What i've done is Provided that a!=1

Then used as a fact to prove that when N=1 if also applies then which is impossible since we know b>0

Is that correct?

Thanks!