Geodesic
Pell's equation without irrational numbers
Journal of integer sequences, Tome 13 (2010) no. 4
We give a simple way to generate an infinite number of solutions to Pell's equation $x^{2} - D y^{2} = 1$, 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.
Classification : 11D09, 11E16
Keywords: pell's equation, quadratic form, stern-brocot tree, universal geometry 
@article{JIS_2010__13_4_a6,
     author = {Wildberger,  N.J.},
     title = {Pell's equation without irrational numbers},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {4},
     zbl = {1278.11041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_4_a6/}
}
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Wildberger,  N.J. Pell's equation without irrational numbers. Journal of integer sequences, Tome 13 (2010) no. 4. http://geodesic.mathdoc.fr/item/JIS_2010__13_4_a6/