Journal of Integer Sequences, Vol. 13 (2010), Article 10.4.3

Pell's Equation without Irrational Numbers

N. J. Wildberger
School of Mathematics and Statistics
UNSW Sydney


We give a simple way to generate an infinite number of solutions to Pell's equation x2 - D y2 = 1, requiring only basic matrix arithmetic and no knowledge of irrational numbers. We illustrate the method for D = 2,7 and 61. Connections to the Stern-Brocot tree and universal geometry are also discussed.

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Received December 21 2009; revised versions received March 22 2010. Published in Journal of Integer Sequences, March 23 2010.

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