Results 1 to 3 of 3

Math Help - LCM and HCD

  1. #1
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    541

    LCM and HCD

    Find all naturels numbers a , b :

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by dhiab View Post
    Find all naturels numbers a , b :

    Since 1996 - 49\Delta^2 = 2m^2 it is clear that \Delta must be even. If \Delta=2 then m=30. If \Delta=4 or 6 then \tfrac12(1996 - 49\Delta^2) is not a perfect square, and if \Delta\geqslant8 then \tfrac12(1996 - 49\Delta^2) is negative.

    So the only possibility is that a and b have lcm 30 and gcd 2. From there, you should be able to list the possible values of a and b.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    541
    Quote Originally Posted by Opalg View Post
    Since 1996 - 49\Delta^2 = 2m^2 it is clear that \Delta must be even. If \Delta=2 then m=30. If \Delta=4 or 6 then \tfrac12(1996 - 49\Delta^2) is not a perfect square, and if \Delta\geqslant8 then \tfrac12(1996 - 49\Delta^2) is negative.

    So the only possibility is that a and b have lcm 30 and gcd 2. From there, you should be able to list the possible values of a and b.
    Hello : Thank you. are you the details ?
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum