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.

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:

.

See alsoEdit

ReferencesEdit

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