Indeterminate Equation

an equation that contains 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 indeterminate systems of equations as a rule have an infinite number of solutions. The term “indeterminate equation” is used in number theory, where we are interested in the solutions of indeterminate equations that satisfy various arithmetic conditions (indeterminate equations are usually solved for integral or rational values). The study of these solutions constitutes the subject of the theory of Diophantine equations.