Results 1 to 2 of 2

Math Help - Finding infinite set of solutions, X and Y

  1. #1
    RAz
    RAz is offline
    Junior Member RAz's Avatar
    Joined
    May 2008
    From
    Canada
    Posts
    54

    Finding infinite set of solutions, X and Y

    Q. Find an infinite set of integers x any y such that 4973x+9743y=h. Write answer in terms of the arbitrary integer L (Lambda, hehe).

    Here's what I've got:

    (i) First find HCF

    (after euclidean algorithm) = 1.

    (ii) Find x and y integers
    1=203-202
    1=203-(4770-4669)
    1=(24)203-4770
    1=24(4973-4770)-4770
    1=24(4973)-25(4770)
    1=24(4973)-25(9743-4973)
    1=24(4973)-25(9743+25(4973))
    1=40(4973)+9743(-25)

    So x = 29 and y = -25 (it is already wrong, LHS does not = RHS)

    But I persisted

    (iii) X = 49 + 9743L (lambda), Y=-25-4973L
    eg let L = 100

    Oh dear it's wrong :C

    Any help on this? I think I stuffed up during the arithmetic, as usual
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello RAz
    Quote Originally Posted by RAz View Post
    1=203-202
    1=203-(4770-4669)
    You went wrong on line 2! Here's what I got:

    1 = 203 - 2 . 101

    = 203 - 2 . (4770 - 23 . 203)

    = 47 . 203 - 2 . 4770

    = 47 . (4973 - 4770) - 2 . 4770

    = 47 . 4973 - 49 . 4770

    = 47 . 4973 - 49 . (9743 - 4973)

    = 96 . 4973 - 49 . 9743

    So x = 96 + 9743\lambda and y = -49 - 4973\lambda

    Grandad

    Last edited by Grandad; March 25th 2009 at 10:14 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. infinite solutions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 14th 2011, 04:57 AM
  2. Replies: 1
    Last Post: September 1st 2009, 06:22 PM
  3. Infinite Solutions
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: July 11th 2009, 04:30 PM
  4. Infinite Number of Solutions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 8th 2009, 11:09 PM
  5. Infinite Solutions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 4th 2008, 05:49 AM

Search Tags


/mathhelpforum @mathhelpforum