On the Diophantine equations z(2)=f(x)(2)+/- f(y)(2) involving quartic polynomials

Zhang, Y; Zargar, AS

Zhang, Y (reprint author), Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.

PERIODICA MATHEMATICA HUNGARICA, 2019; 79 (1): 25

Abstract

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 ......

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