Erdős Problem 896

### What is the conjecture

https://www.erdosproblems.com/896

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 $b\in B$).

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Read the Erdős Problems entry for conjecture 896 first, then inspect how existing conjectures are formalized in this repository. The work is complete when the conjecture has a suitable Lean formalization and the repository's relevant checks pass.

Written by the indexing model from the issue text.