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# Linear integer problem

Posted on 2012-09-07
Medium Priority
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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.
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Question by:InteractiveMind

LVL 27

Accepted Solution

d-glitch earned 1500 total points
ID: 38376977
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.
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LVL 25

Author Comment

ID: 38382213
Your hint of it being a Diophantine Equation helped.
Here I found a general solution for precisely this class of problem:
http://mathforum.org/library/drmath/view/66870.html

Thanks.
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