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Equation with two variables

  1. Jan 9, 2014 #1
    Find all the positive integer solutions where x and y are odd numbers, to the equation: 17x+11y=1000

    Attempt of solution:

    First attempt:
    With Diophantine equation have gotten the answers:


    and the general solutions will be:


    Now I don't know what to do.

    Second attempt:
    If I skip the Diophantine solution and do it like this:


    Now I see that x has to be in the interval 0≤x≤58 if y should be positive.

    If I test all the odd numbers in the interval I'll get 3 solutions when both x and y are positive and odd numbers. The solutions are:

    (x, y) = (9, 77), (31, 43) and (53, 9)

    This solutions (which should be the right answer) takes alot of time because you have to test all odd numbers between 0 to 58 (29 different numbers).

    I need help to find an easier solution.
  2. jcsd
  3. Jan 9, 2014 #2


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    Science Advisor
    Homework Helper

    If you don't want to check all those numbers you should use your Diophantine solution. You just have to figure out what values of k will make both x and y positive. There aren't that many.
  4. Jan 10, 2014 #3
    Thanks, that makes sense!

    Then I just have following numbers k= 177, 178, 179, 180, 181 to make x and y positive and only k= 177, 179, 181 to make them positive AND odd.

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