Csaba S'andor

activity

20242026

collaborators

4 papers

math.NT2026

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

Sándor Z. Kiss, Csaba Sándor, 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

Péter Pál Pach, Csaba Sándor

Let $ρ_{k} (N)$ 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 pr…

math.NT2025

Identical representation functions of linear forms

Sándor Kiss, Csaba Sándor

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 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…