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, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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.