Could any one help me to point out some literature/ papers which solves a homogenous linear Diophantine equation (one equation) of the form

$a_1 \times x_1+a_2 \times x_2 + a_3 \times x_3+....+a_n \times x_n=0$, where $a_1,a_2,...,a_n$ are positive or negative integer constants and $x_1,x_2,...,x_n$ are positive integer variables.

Such an equation may have no solution or infinite number of solutions however there must exist be some minimal solutions or a set of base solutions which can be used to derive ALL other solutions of the equation.

1) Could you point out some work/literature which tries to find the set of base solutions of the above equation.

Thanks in advance.

  • $\begingroup$ Reduce to the case where the $x_i$ are coprime and go from there. $\endgroup$ Jun 30, 2014 at 5:27

1 Answer 1


Try this one on Google,

Parametric Solution of Linear Homogeneous Diophantine Equations by Wallace Givens.

  • $\begingroup$ Huh. I think I reviewed this too hastily. Thanks for mentioning that. (I'll delete the above comment.) $\endgroup$ Jun 30, 2014 at 6:56
  • $\begingroup$ Heh, I just saw your Comment on another Q about Google not working in your location, so I've deleted my Comment as well. $\endgroup$
    – hardmath
    Jun 30, 2014 at 11:48
  • $\begingroup$ Please try to describe as much here as possible in order to make the answer self-contained. Links are fine as support, but they can go stale and then an answer which is nothing more than a link loses its value. $\endgroup$
    – robjohn
    Jul 2, 2014 at 22:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.