Random Thue and Fermat equations
نویسندگان
چکیده
منابع مشابه
Thue Equations and Elliptic Curves
We discuss estimates for the number of solutions of Thue equations and for the number of twists of elliptic curves over the rationals with rank at least 2. We indicate some of the connections between these problems. 1. THUE EQUATIONS Let F be a binary form with rational integer coefficients and with r ≥ 3. Let h be a non-zero integer. In 1909, Thue [43] proved that if F is irreducible then the ...
متن کاملThue equations and CM-fields
We obtain a polynomial type upper bound for the size of the integral solutions of Thue equations F (X,Y ) = b defined over a totally real number field K, assuming that F (X, 1) has a root α such that K(α) is a CM-field. Furthermore, we give an algorithm for the computation of the integral solutions of such an equation.
متن کاملSolubility of Fermat Equations
The arithmetic of the equation a1x d 1 + a2x d 2 + a3x d 3 = 0 is considered for d > 2, with the outcome that the set of coefficients for which the equation admits a non-zero integer solution is shown to have density zero.
متن کاملSOLVING FERMAT - TYPE EQUATIONS x
In this paper, we are interested in solving the Fermat-type equations x5 + y5 = dzp, where d is a positive integer and p a prime number ≥ 7. We describe a new method based on modularity theorems which allows us to improve all earlier results for this equation. We finally discuss the present limits of the method by looking at the case d = 3.
متن کاملParametrized Thue Equations — A Survey
We consider families of parametrized Thue equations Fa(X, Y ) = ±1, a ∈ , where Fa ∈ [a][X,Y ] is a binary irreducible form with coefficients which are polynomials in some parameter a. We give a survey on known results. 1 Thue Equations Let F ∈ Z[X, Y ] be a homogeneous, irreducible polynomial of degree n ≥ 3 and m be a nonzero integer. Then the Diophantine equation F (X, Y ) = m (1) is called ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2015
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa167-2-6