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indeterminate equation : ウィキペディア英語版
indeterminate equation
An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2''x'' = ''y'' is a simple indeterminate equation, as are a''x'' + b''y'' = c and ''x''2 = 1. Indeterminate equations cannot be solved uniquely. Prominent examples include the following:
Univariate polynomial equation:
:a_nx^n+a_x^+\dots +a_2x^2+a_1x+a_0 = 0,
which has multiple solutions for the variable ''x'' in the complex plane unless it can be rewritten in the form a_n(x-b)^n=0.
Non-degenerate conic equation:
:Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0,
where at least one of the given parameters ''A'', ''B'', and ''C'' is non-zero, and ''x'' and ''y'' are real variables.
Pell's equation:
:\ x^2 - Py^2 = 1,
where ''P'' is a given integer that is not a square number, and in which the variables ''x'' and ''y'' are required to be integers.
The equation of Pythagorean triples:
:x^2+y^2=z^2,
in which the variables ''x'', ''y'', and ''z'' are required to be positive integers.
The equation of the Fermat–Catalan conjecture:
:a^m+b^n=c^k,
in which the variables ''a'', ''b'', ''c'' are required to be coprime positive integers and the variables ''m'', ''n'', and ''k'' are required to be positive integers the sum of whose reciprocals is less than 1.
== See also ==

* Indeterminate system
* Indeterminate (variable)
* Linear algebra

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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