Csaba Sándor

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20162023

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8 papers · 1 filter

math.NT2024

On the largest value of the solutions of Erdős's last equation

István Pink, Csaba Sándor

Let $n$ be a positive integer. The Diophantine equation $n (x_{1} + x_{2} + \dots + x_{n}) = x_{1} x_{2} \dots x_{n}$ , $1 \leq x_{1} \leq x_{2} \leq \dots \leq x_{n}$ is called Erdős's last equation. We prove that…

math.NT2023

Representation functions in the set of natural numbers

Shi-Qiang Chen, Csaba Sándor, Quan-Hui Yang

Let $N$ be the set of all nonnegative integers. For $S \subseteq N$ and $n \in N$ , let $R_{S} (n)$ denote the number of solutions of the equation $n = s + s^{'}$ , $s…

math.NT2023

Multiplicative complements II

Anett Kocsis, Dávid Matolcsi, Csaba Sándor +1

In this paper we prove that if $A$ and $B$ are infinite subsets of positive integers such that every positive integer $n$ can be written as $n = ab$ , $a \in A$ , $b \in B$ , then $\displ…

math.NT2023

Unique representations of integers by linear forms

Sándor Z. Kiss, Csaba Sándor

Let $k \geq 2$ be an integer and let $A$ be a set of nonnegative integers. For a $k$ -tuple of positive integers $λ = (λ_{1}, \dots, λ_{k})$ with $1 \le λ_{1} < λ_{2} < \d…

math.NT2023

On monotone increasing representation functions

Sándor Z. Kiss, Csaba Sándor, Quan-Hui Yang

Let $k \geq 2$ be an integer and let $A$ be a set of nonnegative integers. The representation function $R_{A, k} (n)$ for the set $A$ is the number of representations of a nonnegative…

math.NT2023

On a problem of Nathanson related to minimal asymptotic bases of order $h$

Shi-Qiang Chen, Csaba Sándor, Quan-Hui Yang

For integer $h \geq 2$ and $A \subseteq N$ , we define $h A$ to be all integers which can be written as a sum of $h$ elements of $A$ . The set $A$ is called an asymptotic basis o…

On the largest value of the solutions of Erdős's last equation

Representation functions in the set of natural numbers

Multiplicative complements II

Unique representations of integers by linear forms

On monotone increasing representation functions

On a problem of Nathanson related to minimal asymptotic bases of order h

On a problem of Nathanson related to minimal asymptotic bases of order $h$