On a conjecture of E. Thomas concerning parametrized Thue equations

Abstract

is called Thue equation in honour of A. Thue, who proved in 1909 [19] that the number of its solutions in integers is finite. Thue’s result is not effective, but in 1968, A. Baker [1] gave an upper bound for the solutions using his lower bounds for linear forms in logarithms of algebraic numbers. Since then, algorithms for the solution of single Thue equations have been ∗This work was supported by Austrian National Bank project nr. 7088 and the Austrian-Hungarian Science Cooperation project