Hello and thanks for looking I have to prove the following :Prove that gcd(a,b) = 1 if and only if gcd(ab,a+b)=1 Thanks a lot in advance for the help
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Originally Posted by octagonreturns Hello and thanks for looking I have to prove the following :Prove that gcd(a,b) = 1 if and only if gcd(ab,a+b)=1 Thanks a lot in advance for the help Let then so or . WLOG say then since it means . And so .
Hello, Proving this implication : Let d divides a and d divides b. Therefore, d (and even d˛) divides ab and d divides (a+b). But we know that gcd(ab,a+b)=1. --> d divides 1. So d=1.
Thank you all so very much for your time and help!
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