On the Extended 1-2-3 Conjecture of Pilz

Abstract

We resolve (for all sufficiently large $n$) a conjecture of Pilz on the symmetric difference $AΔ(2A)Δ\cdotsΔ(nA)$ for finite sets $A\subseteq \mathbb{N}$ of positive integers. We show that this set always has cardinality at least $n$ for large $n$.