OPEN
This is open, and cannot be resolved with a finite computation.
Can every integer $N\geq 2$ be written as\[N=\frac{\prod_{1\leq i\leq k}(m+i)}{\prod_{1\leq i\leq k}(n+i)}\]for some $k\geq 2$ and $m\geq n+k$?
If $n$ and $k$ are fixed then can one say anything about the set of integers so represented?
See also
[677].
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T. F. Bloom, Erdős Problem #686, https://www.erdosproblems.com/686, accessed 2026-01-16
