Tuesday, 30 June 2015

linear algebra - Prove that: If ninmathbbZmsetminusleft0right has a multiplicative inverse, then this is definitely unique




Prove that: If nZm{0} for
mN has a multiplicative inverse, then this is
definitely unique.




I don't know where we can start with this proof but I think it's important to know that nZm has got a multiplicative inverse in Zm if and only if the gcd (n,m)=1. That's what I have learned some days ago here, from many answers.




Maybe it's somehow possible to deduce it from this fact in order to prove it? Because that's what comes to my mind when we talk about multiplicative inverses :P


Answer



Hint If k,l are multiplicative inverses of n then what is
knl=?


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