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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.

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  • $\begingroup$ Reduce to the case where the $x_i$ are coprime and go from there. $\endgroup$ – Adam Hughes Jun 30 '14 at 5:27
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Try this one on Google,

Parametric Solution of Linear Homogeneous Diophantine Equations by Wallace Givens.

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  • $\begingroup$ Huh. I think I reviewed this too hastily. Thanks for mentioning that. (I'll delete the above comment.) $\endgroup$ – Rebecca J. Stones Jun 30 '14 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 '14 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 '14 at 22:02

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