Algorithm to solve certain ternary quartic Diophantine equations

Authors: LASZLO SZALAY

Abstract: In this paper, we develop an algorithm to solve completely the Diophantine equation F(x,y)=z^2, where the quartic inhomogeneous polynomial F(x,y) with integer coefficients satisfies certain technical conditions. The procedure is an extension of the version of Runge's method given by Poulakis.

Keywords: Diophantine equation, Runge method, inhomogeneous ternary equation

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