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 are and. 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.
The equation of the Fermat–Catalan conjecture:
in which the variables ', ', ' are required to be coprime positive integers, and the variables ', ', and ' are required to be positive integers satisfying the following equation:
