Mailles et ensembles de Sidon

TL;DR

This paper examines the grid condition, a necessary criterion for Sidon sets, demonstrating its limitations and providing stronger conditions to better characterize Sidon sets of integers.

Contribution

The paper clarifies the limitations of the grid condition and introduces stronger criteria for identifying Sidon sets of integers.

Findings

The grid condition is neither sufficient nor improvable for Sidon sets.

Stronger conditions than the grid condition are proposed.

Explanations are provided for the limitations of the grid condition.

Abstract

Grid condition and Sidon sets. The grid condition stated by the author in 1957 as a necessary condition for a set of integers to be a Sidon set is neither improvable nor sufficient ; explanations and stronger statements are provided.