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arXiv · 2409.15075

A sumset version of a conjecture of Pilz

János Nagy·Péter Pál Pach
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Abstract

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 $\{a_1,2a_1,\dots,na_1\},\dots, \{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values appear an odd number of times. In this short note we consider a variant of this problem. Namely, we show that in the sumset $\{a_1,2a_1,\dots,na_1\}+\dots+\{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values appear an odd number of times.

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János Nagy, Péter Pál Pach. 2024-09-23. A sumset version of a conjecture of Pilz. https://arxiv.org/abs/2409.15075

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