Erdős Problem #425
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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A finite set has distinct pairwise products if \(ab = cd\), for elements satisfying \(a < b\) and \(c < d\), implies \((a,b) = (c,d)\).
The maximum cardinality \(F(n)\) of a subset of \(\{1,\ldots,n\}\) with distinct pairwise products.
For `r`, all products over `r` distinct elements of `A` are distinct. We use finite subsets of `A` of cardinality exactly `r`.
Attempts
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Exact strict-pair values F(1),...,F(61) are exhaustively verified with standalone checkers and independent SAT controls; the asymptotic constant and higher-r bound remain open, with the missing unifor
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