Indeterminate equation

In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation is a simple indeterminate equation, as is . 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 in the complex plane—unless it can be rewritten in the form . Non-degenerate conic equation: where at least one of the given parameters , , and is non-zero, and and are real variables. Pell's equation: where is a given integer that is not a square number, and in which the variables and are required to be integers. The equation of Pythagorean triples: in which the variables , , and are required to be positive integers.