How to find all integer solution of an equation?

Question

I want to find whether a given equation like $2x + 5y = 27$ (tow variable linear equation) have integer solution for $x$ and $y$, $x\geq 0, y\geq 0$.

If yes how to find it?

And In my actual question i have to find a solution such that $x+y$ is minimized.

Is there a particular method for this or we have to check for all value?

Probably been asked, and answered, a dozen times on this website, but maybe not so easy to find. Suggest searching questions tagged "linear diophantine eqns". — Gerry Myerson, Nov 02 '16 at 08:04
I just need method for this i am implementing this in c++ program so calculation will no matter.. — Poojan Patel, Nov 02 '16 at 08:06
See http://math.stackexchange.com/questions/1995686/proving-that-there-is-no-integer-solution-to-3996x-3071y-482 — lab bhattacharjee, Nov 02 '16 at 08:06
I am doing if i will find solution i needed i delete this question thanks.. — Poojan Patel, Nov 02 '16 at 08:09
No, Poojan, if you find the solution you need, post a link to it. — Gerry Myerson, Nov 04 '16 at 01:48

score 1 · Answer 1 · edited Apr 13 '17 at 12:21

1

Try this link: How to find solutions of linear Diophantine ax + by = c? The mathematical answer to your question lies there, although I suspect it will be somewhat more complicated to efficiently implement this in code.

edited Apr 13 '17 at 12:21

Community

answered Nov 02 '16 at 08:57

user3460322

1 Answers1