A family of quartic Thue inequalities
A family of quartic Thue inequalities
We prove that the only primitive solutions of the Thue inequality |x^4-4cx^y+(6c+2)x^2y^2+4cxy^3+y^4| =4 is an integer, are (x, y)=(+-1, 0), (0, +-1), (1, +-1), (-1, +-1), (+-1, -+2), (+-2, +-1). Solving Thue equations F(x, y)=m of the special type, using the method of Tzanakis, reduces to solving the system of …