A class of fruit Diophantine equations.

We investigate the solvability of a class of Diophantine equations y 2 + z 2 + B = A x 3 + x y z , defined over the set of integers Z where A and B are positive integers with certain conditions. As a consequence, we obtain a family of elliptic curves whose torsion subgroup of Mordell–Weil group over Q is trivial. [ABSTRACT FROM AUTHOR]