A problem of Cameron and Erdős.

This is resolved as a consequence of results of Saxton and Thomason [SaTh15] - they prove that there number of Sidon sets in $\{1,\ldots,N\}$ is at least $2^{(1.16+o(1))N^{1/2}}$. Since each Sidon set is contained in a maximal Sidon set, and each maximal Sidon set contains at most $2^{(1+o(1))N^{1/2}}$ Sidon sets, it follows that\[A_1(N) \geq 2^{(0.16+o(1))N^{1/2}}.\]See also [861].

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This page was last edited 28 December 2025.