Discrete math deals with whole numbers of things. So when we want to solve equations, we usually are looking for integer solutions. Equations which are intended to only have integer solutions were first studied by in the third century by the Greek mathematician Diophantus of Alexandria, and as such are called Diophantine equations. Probably the most famous example of a Diophantine equation is \(a^2 + b^2 = c^2\text{.}\) The integer solutions to this equation are called Pythagorean triples. In general, solving Diophantine equations is hard (in fact, there is provably no general algorithm for deciding whether a Diophantine equation has a solution, a result known as Matiyasevich's Theorem). We will restrict our focus to linear Diophantine equations, which are considerably easier to work with.
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