OPEN
This is open, and cannot be resolved with a finite computation.
Let $A\subset \mathbb{N}$ be an infinite set such that, for any $n$, there are most $2$ solutions to $a+b=n$ with $a\leq b$. Must\[\liminf_{N\to\infty}\frac{\lvert A\cap \{1,\ldots,N\}\rvert}{N^{1/2}}=0?\]
If we replace $2$ by $1$ then $A$ is a Sidon set, for which Erdős proved this is true.
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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #158, https://www.erdosproblems.com/158, accessed 2026-01-18
