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 \(g \geq 2\), 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.