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_14a414673be11d68"}
- id
- vea_5dce9527cd31c536
- frontier
- Erdős problems frontier
- source
- vs_0a40920d142fb8cc
- finding
- vf_4be95d2df14f26a5
finding binding
boundopen_question
Erdős Problem #397 has status 'disproved (lean)'. Statement: Are there only finitely many solutions to $$ \prod_i \binom{2m_i}{m_i}=\prod_j \binom{2n_j}{n_j} $$ with the $m_i,n_j$ distinct? Somani, using ChatGPT, has given a negative answer. In fact, for any $a\geq 2$, if $c=8a^2+8a+1$, $\binom{2a}{a}\binom{4a+4}{2a+2}\binom{2c}{c}= \binom{2a+2}{a+1}\binom{4a}{2a}\binom{2c+2}{c+1}.$ Further families of solutions are given in the comments by SharkyKesa. This was earlier asked about in a [MathOverflow] question, in response to which Elkies also gave an alternative construction which produces solutions - at the moment it is not clear whether Elkies' argument gives infinitely many solutions (although Bloom believes that it can). This was formalized in Lean by Wu using Aristotle. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_14a414673be11d68
vs_0a40920d142fb8cc
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_14a414673be11d68"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_d16778a89da8a832
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_d70e21b7740d53c9finding.assertedCandidate claim vc_14a414673be11d68 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_55faa6f9200b06c3finding.addCandidate claim vc_14a414673be11d68 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.