OPEN
This is open, and cannot be resolved with a finite computation.
Estimate the maximum of $F(A,B)$ as $A,B$ range over all subsets of $\{1,\ldots,N\}$, where $F(A,B)$ counts the number of $m$ such that $m=ab$ has exactly one solution (with $a\in A$ and $b\in B$).
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In the comments van Doorn proves\[(1+o(1))\frac{N^2}{\log N}\leq \max_{A,B}F(A,B) \ll \frac{N^2}{(\log N)^\delta(\log\log N)^{3/2}}\]where $\delta=1-\frac{1+\log\log 2}{\log 2}\approx 0.086$.
See also
[490].
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This page was last edited 06 December 2025. View history
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Additional thanks to: Wouter van Doorn
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 #896, https://www.erdosproblems.com/896, accessed 2026-04-11
