Results 1 to 2 of 2

Math Help - Greatest Common Divisor of (9m+8, 6m+5)

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    29

    Greatest Common Divisor of (9m+8, 6m+5)

    I have a task where I need to calculate the greatest common divisor of (9m+8, 6m+5)
    for all m (m is an integer).

    It would seem that the answer is 1, but I need a sufficient way to prove it. I already know that gcd(a+kb, b) = gcd(a,b) , so gcd(9m+8, 9) = gcd(6m+5, 6) = 1. However, I'm unsure of how to apply this.

    Any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by Koaske View Post
    I have a task where I need to calculate the greatest common divisor of (9m+8, 6m+5)
    for all m (m is an integer).

    It would seem that the answer is 1, but I need a sufficient way to prove it. I already know that gcd(a+kb, b) = gcd(a,b) , so gcd(9m+8, 9) = gcd(6m+5, 6) = 1. However, I'm unsure of how to apply this.

    Any help would be greatly appreciated.
    (9m+8, 6m+5)=(3m+3, 6m+5)=(3m+3, 3m+2)=1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Least common multiple - Greatest common divisor
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: October 25th 2010, 05:45 AM
  2. Greatest Common Divisor.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 23rd 2009, 12:36 AM
  3. Greatest common divisor
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: March 17th 2009, 07:16 PM
  4. greatest common divisor
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 14th 2008, 03:24 AM
  5. greatest common divisor
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 25th 2008, 09:36 AM

Search Tags


/mathhelpforum @mathhelpforum