Definitions

# Indeterminate equation

An indeterminate equation, in mathematics, is an equation for which there is an infinite set of solutions; for example, 2x = y is a simple indeterminate equation. Indeterminate equations cannot be directly solved from the given information. For example, the equations

$ax + by = c$

$x^2 - Py^2 = 1$

where a, b, c, and P are given integers (provided that P is not a square number), are indeterminate equations. Equations of the second form are named Pell's equations.