Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Algebra GCD Proof problem

  1. Sep 21, 2010 #1
    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.
  2. jcsd
  3. Sep 21, 2010 #2
    Re: urgent algebra GCD Proof problem

    Use the Euclidean algorithm.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook