Indeterminate equation

An equation containing more than one unknown. A system of equations in which the number of unknowns is greater than the number of equations is called an indeterminate system of equations. Indeterminate equations and systems have, as a rule, infinitely many solutions. The term "indeterminate equation" is used in number theory, when one is interested in solutions of an indeterminate equation satisfying some arithmetic condition (usually one looks for solutions in integers or rational numbers). The study of such equations forms the topic of the theory of Diophantine equations.