Open Access
June 2000 The negative Pell equation and Pythagorean triples
Aleksander Grytczk, Florian Luca, Marek Wójtowicz
Proc. Japan Acad. Ser. A Math. Sci. 76(6): 91-94 (June 2000). DOI: 10.3792/pjaa.76.91


We give a simple criterion for the solvability in integers of the negative Pell equation $x^2 - dy^2 = -1$ by means of primitive Pythagorean triples. The method of proof allows us to also solve the problem of determinig the fundamental units of negative norm in real quadratic fields.


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Aleksander Grytczk. Florian Luca. Marek Wójtowicz. "The negative Pell equation and Pythagorean triples." Proc. Japan Acad. Ser. A Math. Sci. 76 (6) 91 - 94, June 2000.


Published: June 2000
First available in Project Euclid: 23 May 2006

zbMATH: 0971.11013
MathSciNet: MR1769976
Digital Object Identifier: 10.3792/pjaa.76.91

Primary: 11D09

Keywords: Negative Pell equation , Pythagorean triples

Rights: Copyright © 2000 The Japan Academy

Vol.76 • No. 6 • June 2000
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