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.
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 also
Indeterminate form
Indeterminate system
Indeterminate (variable) Linear algebra