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pro vyhledávání: '"PETHŐ, Attila"'
Consider $k\ge 2$ distinct, linearly independent, homogeneous linear recurrences of order $k$ satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree $k$, and there is a very broad general i
Externí odkaz:
http://arxiv.org/abs/2308.13817
Let $q$ be an integer. A $D(q)$-$m$-tuple is a set of $m$ distinct positive integers ${a_1, a_2, . . . , a_m}$ such that $a_ia_j + q$ is a perfect square for all $1 \leq i < j \leq m$. By counting integer solutions $x \in [1, b]$ of congruences $x^2
Externí odkaz:
http://arxiv.org/abs/2304.01775
Autor:
Pethő, Attila, Tengely, Szabolcs
Publikováno v:
In Journal of Number Theory February 2025 267:34-79
Autor:
Pethő, Attila
Let $(a_n), (b_n)$ be linear recursive sequences of integers with characteristic polynomials $A(X),B(X)\in \mathbb{Z}[X]$ respectively. Assume that $A(X)$ has a dominating and simple real root $\alpha$, while $B(X)$ has a pair of conjugate complex do
Externí odkaz:
http://arxiv.org/abs/2111.11081
Autor:
Hannusch, Carolin, Pethő, Attila
Let $A_{\varphi}$ denote the matrix of rotation with angle $\varphi$ of the Euclidean plane, FLOOR the function, which rounds a real point to the nearest lattice point down on the left and ROUND the function for rounding off a vector to the nearest n
Externí odkaz:
http://arxiv.org/abs/2109.01828
Autor:
Vécsi, Ádám1 (AUTHOR) petho.attila@unideb.hu, Pethő, Attila1 (AUTHOR)
Publikováno v:
Cryptography (2410-387X). Jun2024, Vol. 8 Issue 2, p19. 22p.
Autor:
Pethő, Attila
In these notes we study the $k$-generalized Fibonacci sequences - $(F_n^{(k)})_{n\in \Z}$ - with positive and negative indices. Denote $T_k(x)$ its characteristic polynomial. Our most interesting finding is that if $k$ is even then the absolute value
Externí odkaz:
http://arxiv.org/abs/2008.10899
Let $\mathcal{O}$ be an order, that is a commutative ring with $1$ whose additive structure is a free $\mathbb{Z}$-module of finite rank. A generalized number system (GNS for short) over $\mathcal{O}$ is a pair $(p,\mathcal{D} )$ where $p\in\mathcal{
Externí odkaz:
http://arxiv.org/abs/1810.09710
There are two-dimensional expanding shift radix systems (SRS) which have some periodic orbits. The aim of the present paper is to describe such unusual points as well as possible. We give all regions that contain parameters the corresponding SRS of w
Externí odkaz:
http://arxiv.org/abs/1711.09596