Pell’s equation, DYK Fact 580
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JaneFairfax
Posted: 20:16 Tuesday 21 July 2009


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Did you know? If d is a positive integer which is not a perfect square, then there exist nonzero integers x and y such that x2 − dy2 = 1. The Diophantine equation x2 − dy2 = 1 is known as Pell’s equation. This is what I’ve read about today in A Course in Number Theory by H.E. Rose. ThumbsUp.gif
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algebraic topology
Posted: 09:33 Wednesday 22 July 2009


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Nontrivial solutions to Pell’s equations (i.e. for which y ≠ 0) can be found by calculating the convergents in the continued-fraction expansion of .
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JaneFairfax
Posted: 12:42 Saturday 25 July 2009


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Did you know? An application of Pell’s equation in solving a number-theory problem has been given here. Clapping.gif
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algebraic topology
Posted: 15:57 Saturday 25 July 2009


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Pell’s equation is named after the 17th-century English mathematician John Pell, although it had been studied by the ancient Greeks, Indians and Arabs. It is a particular form of the Pell–Fermat equation, a Diophantine equation of the form , where m is any nonzero integer.
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