Diophantine Equations.

An equation in two or more variables is called a Diophantine equation if only integers solutions are of interest. A linear Diophantine equation takes the form \(a_1x_1 + a_2x_x + \cdots + a_nx_n = b\) for constants \(a_1,\ldots, a_n, b\text{.}\)

A solution to a Diophantine equation is a solution to the equation consisting only of integers.