Diophantine equation

A Diophantine equation, named after the Ancient Greek mathematician Diophantus, is an equation in any number of variables that only admits solutions from the ring of integers, $$\mathbb Z$$. Their study forms a part of the branch of mathematics known as number theory.

Of particular interest are linear Diophantine equations, of the form $$a_1x_1+a_2x_2+\cdots+a_nx_n=b$$, which may be solved by means of the extended Euclidean algorithm.