On additive complement of a finite set

TL;DR

This paper proves a conjecture regarding the additive complement of finite sets of nonnegative integers, showing that their sum covers all sufficiently large integers.

Contribution

It confirms a conjecture by Chen and Fang about the properties of additive complements of finite sets.

Findings

Proves the conjecture of Chen and Fang.

Shows that the sum of the sets covers all large integers.

Advances understanding of additive complements in number theory.

Abstract

We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set.