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.
"Algorithm to solve certain ternary quartic Diophantine equations,"
Turkish Journal of Mathematics: Vol. 37:
5, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss5/1