(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let p be a prime and let n≥2 be an integer. Prove that p^{1/n}is irrational.

2. Relevant equations

We know that for integers a>1 and b such that gcd(a,b)=1, a does not divide b^n for any n≥

1.

3. The attempt at a solution

To prove irrationality, assume p^(1/n)=a/b for integers a and b≠0.

This is equivalent to a^{n}=pb^{n}

If we've assumed a and b have been reduced to lowest terms, gcd(a,b)=1.

Then the proof by contradiction would follow directly if it were just a=pb^{n}

But what do I do since it's a^{n}?

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# Homework Help: Relatively prime integer proof

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