P. Pach

activity

20242026

collaborators

4 papers

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

On the density of Kravitz sets

Vsevolod Lev, Máté Matolcsi, Péter Pál Pach +1

We show that for a subset $A$ of the cyclic group of prime order $p > 3$ , if the sumset $A + A - 2 A$ is not the whole group, then $∣ A ∣ \leq \frac{2}{7} p$ . Besides combinatorial arguments, we…

math.CO2025

Equidistribution of subset sums

Péter Pál Pach

We answer a question of Katona and Makar-Limanov, by showing that in an abelian group of order $2 h$ the $h$ -element subset sums are asymptotically (as $h \to \infty$ ) equidistribute…

math.CO2024

A sumset version of a conjecture of Pilz

János Nagy, Péter Pál Pach

Pilz's conjecture states that for any finite set $A = {a_{1}, a_{2}, \dots, a_{k}}$ of positive integers and positive integer $n$ in the union of the sets $\{a_1,2a_1,\dots,na_1\},\dots, \{…