(adsbygoogle = window.adsbygoogle || []).push({}); urgent algebra GCD Proof problem

1. The problem statement, all variables and given/known data

let d=gcd(m,n). Prove that d=am+bn, where a,b are integers.

2. Relevant equations

use of induction and euclidean algorithm.

3. The attempt at a solution

i know when d being a generator and d=am+bn where m,n are generators, then d=gcd(m,n).

But i got stuck when proving the converse(which is the problem statement above).

I use the iterative algorithm(i.e. "n=qm+r";gcd(m,n)=gcd(m,r) and so on) but just does not work. And i do not know how to use "induction" in this proof.

Thank you for helping me.

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# Algebra GCD Proof problem

**Physics Forums | Science Articles, Homework Help, Discussion**