1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Greatest common divisor

  1. Nov 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppsoe a, b[tex]\in[/tex]natural numbers, and d=GCD(a,b). Then d^2=GCD(a^2,b^2). I need to find where the proof goes wrong.

    2. Relevant equations

    3. The attempt at a solution
    By hypothesis, we have that d divides a and d divides b, so there are integres s and t with a=ds and b=dt. Then a^2=d^2s^2 and so d^2 divides a^2. Similarily d^2 divides b^2. Thus d^2 is a common divisor of a^2 and b^2, as desired.
  2. jcsd
  3. Nov 17, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Re: d^2=GCD(a^2,b^2)

    No, not "as desired". What you "desire" is the greatest common divisor. Saying that d^2 is a common divisor does not mean it is the GREATEST common divisor.
  4. Nov 17, 2008 #3
    Re: d^2=GCD(a^2,b^2)

    Ok, that made a lot more sense now that I see that!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Greatest common divisor
  1. Greatest common divisor (Replies: 24)