Some remarks on the diophantine equation $(x^2 - 1)(y^2 - 1) = (z^2 - 1)^2$
Al-Kadhi, Mohammed ; Kihel, Omar
Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, p. 155-156 / Harvested from Project Euclid
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In this paper, among other results, we prove that the title equation has finitely many solutions when $x - y = lz$ and $l$ is a fixed integer $\ne 2$. Moreover, all solutions $(x, y, z)$ satisfy $l < z < l^2 / 2$, $1 < y < l^2 / 2$ and $l^2+1 < x < (l^3 + l^2) / 2$. As a consequence, we extend a result of Cao.
Publié le : 2001-12-14
Classification:  Diophantine equation,  11D09,  11D25 
@article{1148392979,
     author = {Al-Kadhi, Mohammed and Kihel, Omar},
     title = {Some remarks on the diophantine equation $(x^2 - 1)(y^2 - 1) = (z^2 - 1)^2$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {77},
     number = {10},
     year = {2001},
     pages = { 155-156},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392979}
}

Al-Kadhi, Mohammed; Kihel, Omar. Some remarks on the diophantine equation $(x^2 - 1)(y^2 - 1) = (z^2 - 1)^2$. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp.  155-156. http://gdmltest.u-ga.fr/item/1148392979/