In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution.
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.
[2] 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
Pell's equation: where
is a given integer that is not a square number, and in which the variables
The equation of Pythagorean triples: in which the variables
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
are required to be positive integers satisfying the following equation:
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