Relation between Primes: Proving (2m-1, 2mn-1/2m-1) = 1

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SUMMARY

The discussion centers on proving that if \( m \) and \( n \) are two distinct prime numbers, then the greatest common divisor (gcd) of \( (2m - 1) \) and \( \frac{2mn - 1}{2m - 1} \) equals 1. Participants clarify that since \( m \) and \( n \) are coprime, it is indeed valid to state that their gcd is 1. The conversation also addresses potential typographical errors regarding the expression \( \frac{2mn - 1}{2m - 1} \), ensuring clarity in mathematical notation.

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helgamauer
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Prove, that if
(m,n) = 1 // m and n are two different primes
then
(2m -1, 2mn -1/2m -1) = 1
 
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1: If m and n are two different primes then isn't it redundant to say their gcd is 1?

2: Do you really mean to say the gcd of an integer and a rational = 1? Or is 1/2^m a typographical error or do you mean something else by that?
 

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