Automatic solution of families of Thue equations and an example of degree 8

We describe a procedure implemented in Mathematica® to solve parametrized families of Thue equations Fn(X,Y)=±1, where Fn is a binary irreducible form in X and Y of degree d≥3 whose coefficients are polynomials in the parameter n. This procedure uses Baker’s method and asymptotic expansions of the quantities involved with exact remainder terms. As an example, we solve a family of degree 8.