On the System of Diophantine Equations X2 - 6y2 = -5 and x= 2z2 - 1.
We show that for all integers and there are no non-trivial solutions of Thue equationsatisfying the additional condition .
The two related Diophantine equations: and , have infinitely many nontrivial, primitive integral solutions. We give two parametric solutions, one for each of these equations.