Pell's equation
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Etymology edit
Named by Leonhard Euler after the 17th-century mathematician John Pell, whom Euler mistakenly believed to be the first to find a general solution.[1]
Noun edit
Pell's equation (plural Pell's equations)
- (number theory) The Diophantine equation for a given integer m, to be solved in integers x and y.
- 1974, Allan M. Kirch, Elementary Number Theory: A Computer Approach, Intext Educational Publishers, page 212:
- 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.
- 1989, Mathematics Magazine, Volume 62, Mathematical Association of America, page 258:
- Thus satisfies Pell's equation and so by Lemma 1, is a convergent to .
- 2013, John J. Watkins, Number Theory: A Historical Approach, Princeton University Press, page 409:
- We introduced Pell's equation
in Chapter 4 as an example of a Diophantine equation. The solution of the Pell equation was used in India in the fourth century to produce the fraction as an excellent rational approximation for .
It is easy to see why solutions to Pell's equation can be used to approximate solutions to —this was known to Archimedes, who used this method to approximate square roots.
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Diophantine equation
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Further reading edit
- Pell's equation on Wikipedia.Wikipedia
- Pell number on Wikipedia.Wikipedia