The system of Diophantine equations (u - 2) x^2- 4uy^2= -12u - 8 and (u + 2) x^2- 4uz^2= -12u + 8

Let be an odd integer. The three numbers and have the property that the product of any two distinct, increased by , is a perfect square. That property allows the solvability of the Diophantine quations and . The integers solutions of the system of these two equations are given by , , , , , . We prove with the aid of simultaneous rational approximations and linear forms in logarithms of quadratic numbers that there is no other solution.