Real Analysis Proof: Prove mn=1 => m=1 & n=1 or m=-1 & n=-1

johnjuwax
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Prove or disprove that if m and n are integers such that mn = 1 then either m= 1 & n = 1 or else m = -1 & n = -1.
 
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What have you already tried and where are you stuck?

Petek
 
Have you tried to find any counterexamples? Usually that will either disprove the statement or give you a reason why no such counterexamples exist.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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