OPEN
This is open, and cannot be resolved with a finite computation.
Find some reasonable function $f(n)$ such that, for almost all integers $n$, the least integer $m$ such that $m\nmid \binom{2n}{n}$ satisfies\[m\sim f(n).\]
Disclaimer: The open status of this problem reflects the current belief of the owner of this website. There may be literature on this problem that I am unaware of, which may partially or completely solve the stated problem. Please do your own literature search before expending significant effort on solving this problem. If you find any relevant literature not mentioned here, please add this in a comment.
A problem of Erdős, Graham, Ruzsa, and Straus
[EGRS75], who say it is 'not hard to show that', for almost all $n$, the minimal such $m$ satisfies\[m=\exp((\log n)^{1/2+o(1)}).\]
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This page was last edited 19 October 2025. View history
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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 #731, https://www.erdosproblems.com/731, accessed 2026-04-11
