On general families of parametrized Thue equations

We consider families of parametrized Thue equations Fa(X,Y ) = ±1, a ∈ N where Fa ∈ Z[a][X,Y ] is a binary irreducible form with coefficients which are polynomials in some parameter a. We give a survey on known results and describe the general shape how such families are usually solved using linear form estimates, and show how this can be done algorithmically. 1991 Mathematics Subject Classification: 11D57, 11Y50

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