# On the structure of sets which have coinciding representation functions

## TL;DR

This paper investigates the structure of sets of nonnegative integers where the number of representations of integers as sums of two distinct elements coincides, providing partial structural descriptions.

## Contribution

It offers a partial characterization of sets with identical representation functions, advancing understanding of their structural properties.

## Key findings

- Identifies conditions under which representation functions coincide.
- Provides partial structural descriptions of such sets.
- Advances theoretical understanding of additive number theory.

## Abstract

For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have coinciding representation functions.