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

First available in Project Euclid: 23 May 2006

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Primary: 11D09: Quadratic and bilinear equations

Negative Pell equation Pythagorean triples


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.

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