The negative Pell equation and Pythagorean triples
Grytczk, Aleksander ; Luca, Florian ; Wójtowicz, Marek
Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, p. 91-94 / Harvested from Project Euclid
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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.
Publié le : 2000-06-14
Classification:  Negative Pell equation,  Pythagorean triples,  11D09 
@article{1148393496,
     author = {Grytczk, Aleksander and Luca, Florian and W\'ojtowicz, Marek},
     title = {The negative Pell equation and Pythagorean triples},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {76},
     number = {10},
     year = {2000},
     pages = { 91-94},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148393496}
}

Grytczk, Aleksander; Luca, Florian; Wójtowicz, Marek. The negative Pell equation and Pythagorean triples. Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, pp.  91-94. http://gdmltest.u-ga.fr/item/1148393496/