A Construction of Modular Generalized Sidon Sets

Abstract

A Sidon set $S$ is a set of integers where the number of solutions to any integer equation $k=k_1+k_2$ with $k_1,k_2\in S$ is at most $2$. If $g\ge 2$, the set $S$ is a generalized Sidon set. We consider Sidon sets modulo $n$, where the solutions to addition of elements are considered under a given modulus. In this note, we give a construction of a generalized Sidon set modulo $n$ from any known Sidon set.