Linear diophantine equation of n variables.
I know how to solve a linear Diophantine equation of 2, 3 variables. But is there a way to solve directly a linear Diophantine equation of n variables. For example using matrix?
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$\begingroup$I guess you'll interested in the following article Linear Diophantine Equations written by William J.Gilbert. It contains the following theorem.
Theorem. To solve the system of linear Diophantine equations $AX=B$, unimodular row reduct $[A^t |I]$ to $[R|T]$, where $R$ is in row-echelon form. Then the system $AX=B$ has a integer solutions if and only if the system $R^tK=B$ has integer solution for $K$, and all the solutions of $AX=B$ are of the form $X=T^tK$.
It also contains one example and one exercise with $3$ variables. So you can compare this with the method you know.
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