Results 11 to 20 of about 84 (68)
An algorithm for solving a certain class of Diophantine equations. I
, 1982 A class of Diophantine equations is defined and an algorithm for solving each equation in this class is developed. The methods consist of techniques for the computation of an upper bound for the absolute value of each solution. The computability of these
D. L. Hilliker
semanticscholar +2 more sources
On power integral bases for certain pure number fields defined by $x^{18}-m$ [PDF]
, 2022 summary:Let $K={\mathbb Q}(\alpha)$ be a number field generated by a complex root $\alpha$ of a monic irreducible polynomial $f(x)=x^{18}-m$, $m\neq \mp 1$, is a square free rational integer.
El Fadil, Lhoussain
core +2 more sources
Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture
Proceedings of the London Mathematical Society, Volume 127, Issue 5, Page 1268-1337, November 2023., 2023 Abstract We offer some theorems, mainly finiteness results, for certain patterns in elliptical billiards, related to periodic trajectories; these seem to be the first finiteness results in this context. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in (0,π)$(0,\pi )$, there are only finitely many ...
Pietro Corvaja, Umberto Zannier
wiley +1 more source
The Separation Properties of Binary Topological Spaces
Advances in Mathematical Physics, Volume 2023, Issue 1, 2023., 2023 In the present study, we introduce some new separation axioms for binary topological spaces. This new idea gives the notion of generalized binary (T0, T1, T2, T3, and T4 spaces) and binary generalized semi (T0, T1, T2, T3, and T4 spaces) using generalized binary open sets and binary generalized semi open sets to investigate their properties.
Xiaoli Qiang +5 more
wiley +1 more source
Elementary Number Theory Problems. Part X – Diophantine Equations [PDF]
, 2023 This paper continues the formalization of problems defined in the book “250 Problems in Elementary Number Theory” by Wacław Sierpiński.Faculty of Computer Science, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur ...
Korniłowicz, Artur
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On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$
Mathematika, Volume 68, Issue 2, Page 344-361, April 2022., 2022 Abstract The primary aim of this paper is to study the generalized Fermat equation x2+y2n=z3p\begin{equation*} x^2+y^{2n} = z^{3p} \end{equation*}in coprime integers x, y, and z, where n⩾2$n \geqslant 2$ and p is a fixed prime. Using modularity results over totally real fields and the explicit computation of Hilbert cuspidal eigenforms, we provide a ...
Philippe Michaud‐Jacobs
wiley +1 more source
Continued Fractions and Hankel Determinants from Hyperelliptic Curves
Communications on Pure and Applied Mathematics, Volume 74, Issue 11, Page 2310-2347, November 2021., 2021 Abstract Following van der Poorten, we consider a family of nonlinear maps that are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus g. Using the connection with the classical theory of J‐fractions and orthogonal polynomials, we show that in the simplest case g = 1 this provides a straightforward ...
Andrew N. W. Hone
wiley +1 more source
Brauer–Manin obstruction for Erdős–Straus surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 746-761, August 2020., 2020 Abstract We study the failure of the integral Hasse principle and strong approximation for the Erdős–Straus conjecture using the Brauer–Manin obstruction.
Martin Bright, Daniel Loughran
wiley +1 more source
Conductor and discriminant of Picard curves
Journal of the London Mathematical Society, Volume 102, Issue 1, Page 368-404, August 2020., 2020 Abstract We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so‐called special Picard curves over Q with good reduction outside 2 and 3, and use this to determine the smallest possible conductor a special Picard curve may have.
Irene I. Bouw +3 more
wiley +1 more source
Computing all elements of given index in sextic fields with a cubic subfield [PDF]
, 2002 summary:It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric family of number fields ...
Járási, István +5 more
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