L. Szalay

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20172026

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6 papers · 1 filter

math.NT2026

Representations with k-generalized Fibonacci numbers

Taboka Prince Chalebgwa, Laszlo Szalay

We study representations of integers using $k$ -generalized Fibonacci numbers. For $k \geq 2$ , we first consider signed representations of zero with coefficients in ${- 1, 0, 1}$ and…

math.NT2025

Four squares from three numbers

Andrej Dujella, László Szalay

We show that there are infinitely many triples of positive integers a, b, c (greater than 1) such that ab + 1, ac + 1, bc + 1 and abc + 1 are all perfect squares.

math.NT2023

Decomposable forms generated by linear recurrences

Kalman Gyory, Attila Petho, Laszlo Szalay

Consider $k \geq 2$ distinct, linearly independent, homogeneous linear recurrences of order $k$ satisfying the same recurrence relation. We prove that the recurrences are related to…

math.NT2020

Markoff-Rosenberger triples and generalized Lucas sequences

Hayder Hashim, László Szalay, Szabolcs Tengely

We consider the Markoff-Rosenberger equation $a x^{2} + b y^{2} + c z^{2} = d x y z$ with $(x, y, z) = (U_{i}, U_{j}, U_{k}),$ where $U_{i}$ denotes the $i$ -th generalized Lucas number of first/second kind. We…

math.NT2020

Resolution of the equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$

Kálmán Liptai, László Németh, Gökhan Soydan +1

Consider the diophantine equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$ in positive integers $x_{1} \leq x_{2}$ , and $y_{1} \leq y_{2}$ . Each side of the equation is a product of two…

math.NT2018

On sunlet graphs connected to a specific map on ${1, 2, \dots, p - 1}$

Omar Khadir, László Németh, László Szalay

In this article, we study the structure of the graph implied by a given map on the set $S_{p} = {1, 2, \dots, p - 1}$ , where $p$ is an odd prime. The consecutive applications of the map g…