On a family of Thue equations of degree 16
نویسنده
چکیده
We consider a parameterized family of Thue equations of degree 16. By a generalization of Tzanakis’ method we reduce this family to a system of Pell equations and linear relations.
منابع مشابه
Effective solution of families of Thue equations containing several parameters
F (X,Y ) = m, where F ∈ Z[X,Y ] is an irreducible form of degree n ≥ 3 and m 6= 0 a fixed integer, has only finitely many solutions. However, this proof is non-effective and does not give any bounds for the size of the possible solutions. In 1968, A. Baker could give effective bounds based on his famous theory on linear forms in logarithms of algebraic numbers. In the last decades, this method ...
متن کاملTo appear in Monatsh. Math. ON EXPLICIT BOUNDS FOR THE SOLUTIONS OF A CLASS OF PARAMETRIZED THUE EQUATIONS OF ARBITRARY DEGREE
In a recent paper [7] the author considered the family of parametrized Thue equations
متن کاملOn a Parametric Family of Thue Inequalities over Function Fields
is called a Thue equation, due to Thue [22] who proved, in the case R = Z, that such an equation has finitely many solutions. In the last decade, starting with the result of Thomas in [21], several families (at the moment up to degree 8; see [9] and the references mentioned therein) of Thue equations have been considered, where the coefficients of the form Fc(X,Y ) depend on an integral paramet...
متن کاملOn Correspondence between Solutions of a Parametric Family of Cubic Thue Equations and Isomorphic Simplest Cubic Fields
We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m+3m+9 and isomorphic simplest cubic fields. By applying R. Okazaki’s result for isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m + 9.
متن کاملOn Correspondence between Solutions of a Parametric Family of Cubic Thue Equations and Non-isomorphic Simplest Cubic Fields
We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m + 3m+ 9 and non-isomorphic simplest cubic fields. By applying R. Okazaki’s result for non-isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m+ 9.
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عنوان ژورنال:
- Math. Comput.
دوره 79 شماره
صفحات -
تاریخ انتشار 2010