About Diophantine Equations z^2=(9\(β\)^2-4)y^2-(4\(β\)^2) - Perrine, Serge (Recent Advances in Mathematical Research and Computer Science Vol. 8, 2022)
We consider the diophantine equation z2=(9\(β\)2-4)y2-(4) and its solutions. The couples (Hn,Nn) where n \(\in\) \(\mathbb{N}\)* and Hn,Nn Horadam numbers built with a second order recurrence give solutions, not all of them. We show the link with Q-matrices, and with the conic relation.