L. Szalay

activity

20142026

most citedDiophantine triples with values in

k

-generalized Fibonacci sequences

8 citations · 25 across the 15 of their papers we have counts for

collaborators

19 papers

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.CO2023★ 1 cited

Schreier Multisets and the $s$ -step Fibonacci Sequences

Hung Viet Chu, Nurettin Irmak, Steven J. Miller +2

Inspired by the surprising relationship (due to A. Bird) between Schreier sets and the Fibonacci sequence, we introduce Schreier multisets and connect these multisets with the $s$ -…

math.CO2021★ 1 cited

Sequences involving square zig-zag shapes

László Németh, László Szalay

We define a so-called square $k$ -zig-zag shape as a part of the regular square grid. Considering the shape as a $k$ -zig-zag digraph, we give values of its vertices according to the…

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…

math.CO2017★ 5 cited

Tilings of hyperbolic $(2 \times n)$ -board with colored squares and dominoes

Takao Komatsu, László Németh, László Szalay

Several articles deal with tilings with squares and dominoes of the well-known regular square mosaic in Euclidean plane, but not any with the hyperbolic regular square mosaics. In…

math.NT2017★ 4 cited

On the Diophantine equation $\sum_{j = 1}^{k} j F_{j}^{p} = F_{n}^{q}$

Gökhan Soydan, László Németh, László Szalay

Let $F_{n}$ denote the $n^{t h}$ term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation $F_{1}^{p} + 2 F_{2}^{p} + \dots + k F_{k}^{p} = F_{n}^{q}$ in the positive integers…

math.CO2017

Power sums in hyperbolic Pascal triangles

László Németh, László Szalay

In this paper, we describe a method to determine the power sum of the elements of the rows in the hyperbolic Pascal triangles corresponding to ${4, q}$ with $q \geq 5$ . The method is…

math.CO2017

Alternating sums in hyperbolic Pascal triangles

László Németh, László Szalay

A new generalization of Pascal's triangle, the so-called hyperbolic Pascal triangles were introduced in [H.B, L.N, L.Sz: Hyperbolic Pascal triangles]. The mathematical background g…

math.NT2017★ 5 cited

Recurrence sequences in the hyperbolic Pascal triangle corresponding to the regular mosaic $\{4,5\}

László Németh, László Szalay

Recently, a new generalization of Pascal's triangle, the so-called hyperbolic Pascal triangles were introduced. The mathematical background goes back to the regular mosaics in the…

math.NT2016

On the $X$ -coordinates of Pell equations which are Tribonacci numbers

Florian Luca, Amanda Montejano, Laszlo Szalay +1

For an integer $d \geq 2$ which is not a square, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^{2} - d Y^{2} = \pm 1$ which is a T…

math.NT2016★ 8 cited

Diophantine triples with values in $k$ -generalized Fibonacci sequences

Clemens Fuchs, Christoph Hutle, Florian Luca +1

We show that if $k \geq 2$ is an integer and $(F_{n}^{(k)})_{n \geq 0}$ is the sequence of $k$ -generalized Fibonacci numbers, then there are only finitely many triples of positive intege…

math.NT2015

Only finitely many Tribonacci Diophantine triples exist

Clemens Fuchs, Christoph Hutle, Nurettin Irmak +2

Diophantine triples taking values in recurrence sequences have recently been studied quite a lot. In particular the question was raised whether or not there are finitely many Dioph…

math.HO2015

Hyperbolic Pascal triangles

Hacene Belbachir, László Németh, László Szalay

In this paper, we introduce a new generalization of Pascal's triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regula…

math.MG2015★ 1 cited

Coincidences in numbers of graph vertices corresponding to regular planar hyperbolic mosaics

László Németh, László Szalay

The aim of this paper is to determine the elements which are in two pairs of sequences linked to the regular mosaics ${4, 5}$ and ${p, q}$ on the hyperbolic plane. The problem le…

math.NT2014

S-Diophantine quadruples with $S = {2, q}$

László Szalay, Volker Ziegler

Let $S$ denote a set of primes and let $a_{1}, \dots, a_{m}$ be positive distinct integers. We call the $m$ -tuple $(a_{1}, \dots, a_{m})$ an $S$ -Diophantine tuple if $a_{i} a_{j} + 1 = s_{i, j}$ are $…

Representations with k-generalized Fibonacci numbers

Four squares from three numbers

Decomposable forms generated by linear recurrences

Schreier Multisets and the s-step Fibonacci Sequences

Sequences involving square zig-zag shapes

Markoff-Rosenberger triples and generalized Lucas sequences

Resolution of the equation (3x1​−1)(3x2​−1)=(5y1​−1)(5y2​−1)

On sunlet graphs connected to a specific map on {1,2,…,p−1}

Tilings of hyperbolic (2×n)-board with colored squares and dominoes

On the Diophantine equation ∑j=1k​jFjp​=Fnq​

Power sums in hyperbolic Pascal triangles

Alternating sums in hyperbolic Pascal triangles

Recurrence sequences in the hyperbolic Pascal triangle corresponding to the regular mosaic $\{4,5\}

On the X-coordinates of Pell equations which are Tribonacci numbers

Diophantine triples with values in k-generalized Fibonacci sequences

Only finitely many Tribonacci Diophantine triples exist

Hyperbolic Pascal triangles

Coincidences in numbers of graph vertices corresponding to regular planar hyperbolic mosaics

S-Diophantine quadruples with S={2,q}

Schreier Multisets and the $s$ -step Fibonacci Sequences

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

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

Tilings of hyperbolic $(2 \times n)$ -board with colored squares and dominoes

On the Diophantine equation $\sum_{j = 1}^{k} j F_{j}^{p} = F_{n}^{q}$

On the $X$ -coordinates of Pell equations which are Tribonacci numbers

Diophantine triples with values in $k$ -generalized Fibonacci sequences

S-Diophantine quadruples with $S = {2, q}$