In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation ax + by =c is a simple indeterminate equation, as is x^2=1. Indeterminate equations cannot be solved uniquely. In fact, in some cases it might even have infinitely many solutions. Some of the prominent examples of indeterminate equations include: Univariate polynomial equation: which has multiple solutions for the variable x in the complex plane—unless it can be rewritten in the form. Non-degenerate conic equation: where at least one of the given parameters A, B, and C is non-zero, and x and y are real variables. Pell's equation: where P is a given integer that is not a square number, and in which the variables x and y are required to be integers. The equation of Pythagorean triples: in which the variables x, y, and z are required to be positive integers. The equation of the Fermat–Catalan conjecture: in which the variables a, b, c are required to be coprime positive integers, and the variables m, n, and k are required to be positive integers satisfying the following equation: