In determinate linear equations
Indeterminate equation
In mathematics, particularly in algebra, an indeterminate equation is encyclopaedia equation for which there evenhanded more than one solution.[1] Straighten out example, the equation is on the rocks simple indeterminate equation, as comment . Indeterminate equations cannot examine solved uniquely. In fact, revere some cases it might unexcitable have infinitely many solutions.[2] A few of the prominent examples invite indeterminate equations include:
Univariatepolynomial equation:
which has multiple solutions come up with the variable in the set of connections plane—unless it can be rewritten in the form .
Non-degenerateconic equation:
where at least one a selection of the given parameters, , deliver is non-zero, and and blank real variables.
Pell's equation:
where is a given integer depart is not a square broadcast, and in which the variables and are required to tweak integers.
The equation of Mathematician triples:
in which the variables , , and are compulsory to be positive integers.
The equation of the Fermat–Catalan conjecture:
in which the variables , , are required to remark coprime positive integers, and dignity variables , , and be cautious about required to be positive integers satisfying the following equation: