Results 1 to 2 of 2

Math Help - After finding d=gcd(a,b,c) how do you go about finding x,y,z so that ax+by+cz=d?

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    79

    Question After finding d=gcd(a,b,c) how do you go about finding x,y,z so that ax+by+cz=d?

    I know how you would find the x,y after finding the gcd of two integers (you basically work backwards through the euclidean algorithm), but I am not sure how to find the x,y,z after finding the gcd of three integers. Could someone tell me the process please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780
    Let d1 = gcd(a, b). Then d = gcd(a, b, c) = gcd(d1, c). There exist x1, y1 such that x1 * a + y1 * b = d1, and there exist x2, y2 such that x2 * d1 + y2 * c = d. Substituting d1 from the second last equation, you can express d as a linear combination of a, b, c.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: December 8th 2011, 10:27 AM
  2. Replies: 1
    Last Post: July 3rd 2010, 10:40 PM
  3. Finding a limit. Finding Maclaurin series.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 18th 2010, 10:04 PM
  4. Finding the radius, solving, and finding theta?
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 13th 2009, 02:37 PM
  5. Replies: 1
    Last Post: April 9th 2009, 09:02 AM

Search Tags


/mathhelpforum @mathhelpforum