Pell's equation
Pell's equation noun: the Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.
Noun
Pell's equation (plural Pell's equations)
- The Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.
- However, due to Euler's mistake in attributing the equation to English mathematician John Pell (1610-1585), Equation (27.14) is called Pell's equation. Results concerning Pell's equation will be stated without proof.1974, Allan M. Kirch, Elementary Number Theory: A Computer Approach, Intext Educational Publishers, page 212
- Thus (P,Q) satisfies Pell's equation and so by Lemma 1, P#47;Q is a convergent to #92;sqrtd.1989, Mathematics Magazine, Volume 62, Mathematical Association of America, page 258
- Synonyms:
- Pell-Fermat equation
Synonyms of Pell's equation
Forms of Pell's equation
| plural | Pell's equations |
|---|---|
| alternative form | Pell equation |
Origin of Pell's equation
Named by Leonhard Euler after the 17th-century mathematician John Pell, whom Euler mistakenly believed to be the first to find a general solution.
Words formed from Pell's equation
- generalised Pell's equation
Questions about Pell's equation
- What does Pell's equation mean?
- Pell's equation means the Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.
- What part of speech is Pell's equation?
- Pell's equation is a noun.
- What is the plural of Pell's equation?
- The plural of Pell's equation is Pell's equations.
Words near Pell's equation in the dictionary
Source and license
Adapted from Wiktionary: Pell's equation (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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