Diophantine equation

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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.

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