Word Pronunciation & Dictionary

pell's equation

Word Rarity Very rare

Frequency: Zipf frequency 1.70 in modern English

Syllables: pel-l's e-qua-tion
IPA

24

Scrabble Score

13

Letters

4

Syllables

11

Unique Chars

Meaning

noun

The Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.

Example Sentences

"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."
"Thus (P,Q) satisfies Pell's equation and so by Lemma 1, P#47;Q is a convergent to #92;sqrtd."
"We introduced Pell's equation #92;qquad#92;qquad#92;qquad#92;qquadx²-ny²#61;1 in Chapter 4 as an example of a Diophantine equation. The solution x#61;577,#92;y#61;408 of the Pell equation x²-2y²#61;1 was used in India in the fourth century to produce the fraction #92;tfrac#123;577#125;#123;408#125; as an excellent rational approximation for #92;sqrt 2. It is easy to see why solutions to Pell's equation can be used to approximate solutions to #92;sqrtn—this was known to Archimedes, who used this method to approximate square roots."

Etymology

Named by Leonhard Euler after the 17th-century mathematician John Pell, whom Euler mistakenly believed to be the first to find a general solution.

Inflected Forms

Pell's equations (plural) Pell equation (alternative)

Phrases

generalised Pell's equation Pell number

Frequently Paired Words

Pell number

Synonyms

Pell-Fermat equation

Questions

What does pell's equation mean?: The Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.
Where does pell's equation come from?: Named by Leonhard Euler after the 17th-century mathematician John Pell, whom Euler mistakenly believed to be the first to find a general solution.

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