Problem Statement
Does there exist a maximal Sidon set $A\subset \{1,\ldots,N\}$ of size $O(N^{1/3})$?
Categories:
Sidon Sets
Progress
A question of Erdős, Sárközy, and Sós [ESS94]. It is easy to prove that the greedy construction of a maximal Sidon set in $\{1,\ldots,N\}$ has size $\gg N^{1/3}$. Ruzsa [Ru98b] constructed a maximal Sidon set of size $\ll (N\log N)^{1/3}$.See also [340].
Source: erdosproblems.com/156 | Last verified: January 13, 2026