Abstract.
In this paper we prove that the only primitive solution of the Thue inequality
\[\left| x^4-2cx^3y+2x^2y^2+2cxy^3+y^4\right| \leq 6c+4,\]
where $c\geq 5$ is an integer, are \(\left(x,y\right)= \left(\pm 1, 0\right), \left(0, \pm 1\right), \left(1, \pm 1\right), \left(-1, \pm 1\right).\)
2010 Mathematics Subject Classification: Primary: 11D25, 11D59, 11A55; Secondary: 11A07, 11B37, 11D75, 11J68, 11J70, 11J86.
