P'eter P'al Pach

activity

20162022

most citedSets avoiding six-term arithmetic progressions in

Z_{6}^{n}

are exponentially small

1 citations · 2 across the 6 of their papers we have counts for

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4 papers · 1 filter

math.NT2019

On the density of sumsets and product sets

Norbert Hegyvári, François Hennecart, Péter Pál Pach

In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.

math.NT2019

Coloring the $n$ -smooth numbers with $n$ colors

Andrés Eduardo Caicedo, Thomas A. C. Chartier, Péter Pál Pach

For which values of $n$ can we color the positive integers with precisely $n$ colors in such a way that for any $a$ , the numbers $a, 2 a, \dots, na$ all get different colors? Pach pose…

math.NT2018

An improved upper bound for the size of the multiplicative 3-Sidon sets

Péter Pál Pach

We say that a set is a multiplicative 3-Sidon set if the equation $s_{1} s_{2} s_{3} = t_{1} t_{2} t_{3}$ does not have a solution consisting of distinct elements taken from this set. In this paper…

math.NT2016

Multiplicative bases and an Erdős problem

Péter Pál Pach, Csaba Sándor

In this paper we investigate how small the density of a multiplicative basis of order $h$ can be in ${1, 2, \dots, n}$ and in $Z^{+}$ . Furthermore, a related problem of Erd\H…

On the density of sumsets and product sets

Coloring the n-smooth numbers with n colors

An improved upper bound for the size of the multiplicative 3-Sidon sets

Multiplicative bases and an Erdős problem

Coloring the $n$ -smooth numbers with $n$ colors