# Indeterminate equation

In mathematics, particularly in algebra, an **indeterminate equation** is an equation for which there is more than one solution.^{[1]}^{[2]} 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.^{[3]} 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.
*

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.
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**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:
*

*.*

## See alsoEdit

## ReferencesEdit

**^**"The Definitive Glossary of Higher Mathematical Jargon — Indeterminate".*Math Vault*. 2019-08-01. Retrieved 2019-12-02.**^**"Indeterminate Definition (Illustrated Mathematics Dictionary)".*www.mathsisfun.com*. Retrieved 2019-12-02.**^**"Indeterminate Equation – Lexique de mathématique". Retrieved 2019-12-02.

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