Linear integer problem

Posted on 2012-09-07
Last Modified: 2012-09-10
Let u,v,w,h,k,l all be integers satisfying

   u*h + v*k + w*l = 0

Given h, k, and l, I wish to generate the set of all u, v, and w with max(u,v,w)<M that satisfy this constraint.

Does anyone have any suggestions? I imagine it's a problem familiar to number theorists.
Question by:InteractiveMind
    LVL 26

    Accepted Solution

    My took An Introduction to the Theory of Numbers in 1970.
    Rusty I am.

    Look at Diophantine Equations.

    All solutions will satisfy       u*h + v*k  =  -( w*l)  =  n*[LCM( h, k, l)]

    If you find the solution for the smallest n where (h, k, l) are relatively prime you may have a start.
    LVL 25

    Author Comment

    Your hint of it being a Diophantine Equation helped.
    Here I found a general solution for precisely this class of problem:


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