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Math Help - Number of Interger value of x and y.

  1. #1
    Junior Member
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    Number of Interger value of x and y.

    How many integer value of x and y are there such that
    4x + 7y = 3 where IxI < 500 and IyI < 500?

    Any help would be appreciated.

    Thanks,
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  2. #2
    Super Member Gamma's Avatar
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    Iowa City, IA
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    All you need to do is find one solution, and you have all of them for this. Let (x_0,y_0) be a solution to ax+by=c.

    Then all other solutions will be of the form:

    x=x_0 + b\left(\frac{k}{gcd(a,b)}\right)
    y=y_0 - a\left(\frac{k}{gcd(a,b)}\right)

    Where k runs through the integers positive and negative.

    So in this case, inspections shows (-1,1) is a solution, so the others are :

    x=-1 + 7(\frac{k}{1})=7k-1
    y=1 - 4(\frac{k}{1})=1-4k

    I trust that you can take it from here
    Last edited by Gamma; August 13th 2009 at 11:29 PM. Reason: TeX error
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