On a Conjecture of E. Thomas concerning parametrized Thue Equations
نویسنده
چکیده
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
منابع مشابه
On Two-Parametric Quartic Families of Diophantine Problems
Let n ≥ 3, v1(x), . . . , vn−1(x) ∈ Z[x] and u ∈ {−1, 1}, then x(x− v1(a)y) · · · (x− vn−1(a)y) + uy = ±1 is called a parametrized familiy of Thue equations, if a ∈ Z and the solutions x, y are searched in Z; cf. Thomas (1993). There are several results concerning parametrized families of cubic and quartic families of Thue equations, see Mignotte et al. (1996) and the references therein. Thomas...
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تاریخ انتشار 2000