Problem 329

Erdős Problem #329: declared status 'open'. Formalized: yes. Suppose $A\subseteq \mathbb{N}$ is a Sidon set. How large can$$\limsup_{N\to \infty}\frac{\lvert A\cap \{1,\ldots,N\}\rvert}{N^{1/2}}$$be? Current best: where the number of solutions to $n=a_1+a_2$ with $a_1\leq a_2$ is at most $g$ for all $n$, so that a $B_2[1]$ set is a Sidon set). Prize: no. Tags: number theory.