Csaba S'andor

activity

20242026

collaborators

5 papers

math.NT2026

Cross representations of additive complements of $r$ -th powers

Yuchen Ding, Ben Krause, Csaba SÃ¡ndor +2

Let $N$ be the set of natural numbers and $S_{r} = {1^{r}, 2^{r}, 3^{r}, \dots}$ the set of $r$ -th powers, where $r \geq 2$ is a natural number. Let $\mathcal{W}_r…

math.NT2026

On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity

SÃ¡ndor Z. Kiss, Csaba SÃ¡ndor, Maciej Zakarczemny

We consider the equality of the values of the $n$ th and $k$ th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. For $k < n$ , we prove that this eq…

math.CO2026

Product representations of perfect powers

PÃ©ter PÃ¡l Pach, Csaba SÃ¡ndor

Let $I ¨ _{k} (N)$ denote the maximum size of a set $A \subseteq {1, 2, \dots, N}$ such that no product of $k$ distinct elements of $A$ is a perfect $d$ -th power. In this short note, we p…

math.NT2025

Identical representation functions of linear forms

SÃ¡ndor Kiss, Csaba SÃ¡ndor

For a set of natural numbers $A$ , let $R_{A} (n)$ be the number of representations of a natural number $n$ as the sum of two terms from $A$ . Many years ago, Nathanson studied the co…

math.NT2024

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

IstvÃ¡n Pink, Csaba SÃ¡ndor

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 ErdÅs's last equation. We prove that…