Solving superelliptic Diophantine equations by Baker's method [PDF]
, 1998 Article dans revue scientifique avec comité de lecture.We describe a method for complete solution of the superelliptic Diophantine equation ay^p=f(x). The method is based on Baker's theory of linear forms in the logarithms.
Bilu, Yuri F. +6 more
core +1 more source
On Two-parametric Quartic Families of Diophantine Problems [PDF]
, 1998 Two-parametric quartic Thue equations are completely solved for sufficiently large values of the parameters. Exceptional units are computed in related quartic number fields. The method depends heavily on A.
Tichy, R.F., Pethö, A.
core +1 more source
On the practical solution of the Thue equation [PDF]
, 1989 This paper gives in detail a practical general method for the explicit determination of all solutions of any Thue equation. It uses a combination of Baker's theory of linear forms in logarithms and recent computational diophantine approximation ...
Weger, de, B.M.M. +6 more
core +1 more source
The extension of the D(-k)-pair {k, k+1) to a quadruple [PDF]
, 2022 Let n be a non-zero integer. A set of m positive integers {; ; ; a_1, a_2, ... , a_m}; ; ; is called a D(n)- m-tuple if a_ia_j + n is a perfect square for all 1 1, then d=1.
Fujita, Yasutsugu +2 more
core
Mesure d'indépendance linéaire de logarithmes dans un groupe algébrique commutatif [PDF]
, 2001 J'ai effectué ma thèse sous la direction scientifique de Sinnou David et Michel Waldschmidt.This thesis falls within the theory of linear forms in logarithms. It comprises two parts as well as three annexes.
Gaudron, Eric
core +4 more sources
On the Non-negative Integer Solutions to Diophantine Equations $F_n - F_m = 7^a$ and $F_n - F_m = 13^a$ [PDF]
, 2023 In this paper, we study the solutions of the equation $F_n-F_m=p^a$ where $p$ is either $7$ or $13$ and $n>m\geqslant 0$, $a\geqslant 2$. We confirm the conjecture of Erduvan and Keskin by proving that there is no solutions for this Diophantine equation.
Soufiane, Mezroui, Anouar, Gaha
core +1 more source
Duplications in the k-generalized Fibonacci sequences [PDF]
, 2021 Let k >= 3 be an odd integer. Consider the k-generalized Fibonacci sequence backward. The characteristic polynomial of this sequence has no dominating zero, therefore the application of Baker's method becomes more difficult. In this paper, we investigate
Szalay, László +2 more
core
MESURES D'INDÉPENDANCE LINÉAIRE DE LOGARITHMES DANS UN GROUPE ALGÉBRIQUE COMMUTATIF [PDF]
, 2005 Version définitive.International audienceThis work falls within the theory of linear forms in logarithms over a connected and commutative algebraic group, defined over the field of algebraic numbers $\overline{Q}$. Let $G$ be such a group.
Gaudron, Éric
core +1 more source
Minorations simultanées de formes linéaires de logarithmes de nombres algébriques [PDF]
, 2014 40p.International audienceThis work falls within the theory of linear forms in logarithms over a commutative linear group defined over a number field. We give lower bounds for simultaneous linear forms in logarithms of algebraic numbers, treating both ...
Gaudron, Éric, Éric Gaudron
core +1 more source
Formes linéaires de logarithmes et équations Diophantiennes [PDF]
, 2022 The field of transcendance has a variety of subfields including : the transcendence of individual numbers, algebraic independence, transcendence of functions ( for example, modular forms, the zeta and $j$ functions, etc.
Tiebekabe, Pagdame
core