A parametric family of quartic Thue inequalities (Q538022)

Using an extended version of \textit{J. Worley}'s result [J. Aust. Math. Soc., Ser. A 31, 202--206 (1981; Zbl 0465.10026)] on rational approximations together with \textit{N. Tzanakis}' method [Acta Arith. 64, No. 3, 271--283 (1993; Zbl 0774.11014)] the author shows that the only primitive, integral solutions to the Diophantine inequality \[ |X^4- 2cX^3Y+2X^2Y^2+2cXY^3+Y^4|\leq 6c+4 \] with \(5\leq c \in \mathbb Z\), are \((\pm 1,0),(0,\pm 1),(1,\pm 1)\) and \((-1,\pm 1)\).