Indeterminate equation
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An indeterminate equation is an equation for which there is an infinite set of solutions – for example, 2x = y. A diophantine equation is an indeterminate equation in which both the solution and the terms must be whole numbers. Indeterminate equations cannot be directly solved from the given information. For example, the equations
where a, b, c, and P are given integers (provided that P is not a square number), are indeterminate equations. In general, we are interested in finding integer solutions to these equations. Equations of the first form are called Diophantine equations. Those of the second form are named Pell's equations.
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