A normal linear Diophantine equation would be some: $ax + by = c$ where $a$ and $b$ are constants. Solution can be found using Euclid's Extended Algorithm.
But what about for longer equations such as: $ax + by + cz = d$?
Is there a way to solve these kinds of equations for more than two variables?
It's this question that I've been asking myself. Say that I have some equation:
$aw + bx + cy + dz = e$
Such that $a, b, c, d$ are constants and $w, x, y, z$ are either 0 or 1. I want to be able to show if a solution exists for some $e$.
Of course, there's always the brute force method to solve, but is there anything more elegant?