By the theory of elliptic curves, we prove that the Diophantine equations z2= f(x) 2± f(y) 2 have infinitely many rational solutions for some quartic polynomials, which gives a positive answer to Question 4.3 of Ulas and Togbé (Publ Math Debrecen 76(1–2):183–201,2010) for quartic polynomials. © 2018,...
