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I know how to solve Diophantine equations of the form $ax+by=c$ but how can I solve linear Diophantine equations having more variables. Like what are the integer solutions of $43x+23y-435z+1324w=1$? I tried to substitute $t=43x+23y-435z$ and then solve first $t+1324w=1$ but then I found that as the result depends on another parameter, it won't help to solve the original equation.

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  • $\begingroup$ Are you trying to solve the equation without multiple parameters? $\endgroup$ – Ethan Hunt Apr 14 '16 at 16:33
  • $\begingroup$ There can be multiple parameters. I just want to know all solutions and how to find them. $\endgroup$ – curious Apr 14 '16 at 16:48

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