Let f is an element of Q[X]be a polynomial without multiple roots and with deg(f) >= 2. We give conditions for f(X) - AX(2) + BX + C such that the Diophantine equation f(x)f(y) = f(z)(2) has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we co...
