Hi, I've encountered this exercise which I'm having a hard time proving. It goes like this: Prove that if m and n are natural, then the nth root of m is either integer or irrational. Any help would be greatly appreciated. Thanks.
I would imagine you would start by proving it for m= p, a prime number. That would make it easy to prove "If integer k is not divisible by p then neither is k^{n}" so you could mimic Euclid's proof that [itex]\sqrt{2}[/itex] is irrational. After that, look at products of prime.