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 $a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=b$, which may be solved by means of the extended Euclidean algorithm.