Identical representation functions of linear forms

SÃ¡ndor Kiss; Csaba SÃ¡ndor

paper

Identical representation functions of linear forms

arXiv:2506.03983

Abstract

For a set of natural numbers $A$ , let $R_{A} (n)$ be the number of representations of a natural number $n$ as the sum of two terms from $A$ . Many years ago, Nathanson studied the conditions for the set $A$ and $B$ of natural numbers that are needed to guarantee that $R_{A} (n) = R_{B} (n)$ for every positive integer $n$ . In the last decades, similar questions have been studied by many authors. In this paper, we extend Nathanson's result to representation functions associated to linear forms and we study related problems.