Pell's Equation without Irrational Numbers
N. J. Wildberger
School of Mathematics and Statistics
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.
Full version: pdf,
Received December 21 2009;
revised versions received March 22 2010.
Published in Journal of Integer Sequences, March 23 2010.
Journal of Integer Sequences home page