evidence boundary
supportsfrontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Evidence atom
back to sources{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_aa03ccf08b02d0d0"}
- id
- vea_f4301a3e4b7773b1
- frontier
- Erdős problems frontier
- source
- vs_3d8d18d82dfcec98
- finding
- vf_e693f890fc5a90c7
finding binding
boundopen_question
Erdős Problem #728 has status 'proved (lean)'. Statement: Let $\varepsilon$ be sufficiently small and $C, C' > 0$. Are there integers $a, b, n$ such that $$a, b > \varepsilon n\quad a!\, b! \mid n!\, (a + b - n)!, $$ and $$C \log n < a + b - n < C' \log n ?$$ Note that the website currently displays a simpler (trivial) version of this problem because $a + b$ isn't assumed to be in the $n + O(\log n)$ regime. Barreto and ChatGPT-5.2 have proved that, for any $0 < C_1 < C_2$, there are infinitely many $a, b, n$ with $b = n/2$, $a = n/2 + O(\log n)$, and $C_1 \log n < a + b - n < C_2 \log n$ such that $a! b! \mid n! (a + b - n)!$ This appears to answer the question in the spirit it was intended. This was formalized in Lean by Alexeev using Aristotle. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_aa03ccf08b02d0d0
vs_3d8d18d82dfcec98
review context
unverified1 events
1 reviewable changes and 0 evaluation records target this atom or its bound objects.
statement
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_aa03ccf08b02d0d0"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_01dc86d907fd1b22
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_d9fbe31b8b02a0ebfinding.assertedCandidate claim vc_aa03ccf08b02d0d0 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_e8c20df8fd48d407finding.addCandidate claim vc_aa03ccf08b02d0d0 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.