The board / number theory / #478
Erdős Problem #478
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(p\) be a prime and \[A_p = \{ k! \pmod{p} : 1\leq k<p\}.\] Is it true that \[\lvert A_p\rvert \sim (1-\tfrac{1}{e})p?\]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/478.Prizenone
Topicsnumber theory, factorials
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA210184
Original pageerdosproblems.com/478
Attempts
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Live page status OPEN; it lists a partial proof claimed by Xiyu Hu (submitted by hxypqr on 2026-07-23) and names hxypqr as currently working on the problem, so the mandatory no-duplication rule applie
SKIPPED