Proceedings of the Japan Academy, Series A, Mathematical Sciences

The negative Pell equation and Pythagorean triples

Aleksander Grytczk, Florian Luca, and Marek Wójtowicz

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 6 (2000), 91-94.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393496

Digital Object Identifier
doi:10.3792/pjaa.76.91

Mathematical Reviews number (MathSciNet)
MR1769976

Zentralblatt MATH identifier
0971.11013

Subjects
Primary: 11D09: Quadratic and bilinear equations

Keywords
Negative Pell equation Pythagorean triples

Citation

Grytczk, Aleksander; Luca, Florian; Wójtowicz, Marek. The negative Pell equation and Pythagorean triples. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 6, 91--94. doi:10.3792/pjaa.76.91. https://projecteuclid.org/euclid.pja/1148393496


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