frontiers / frontier
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewErdős Problem #123 remains OPEN. Statement: **Erdős Problem #123** Let $a, b, c$ be three integers which are pairwise coprime. Is every large integer the sum of distinct integers of the form $a^k b^l c^m$ ($k, l, m ≥ 0$), none of which divide any other? Equivalently: is the set $\{a^k b^l c^m : k, l, m \geq 0\}$ d-complete? Note: For this not to reduce to the two-integer case, we need the integers to be greater than one and distinct. Topics: number theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
A proposal; no authority until an accepted review event.
accept gate
0 of 4 on recordtimeline
vpr_69879990bac817fbSEMANTIC-EDGE DRAFT -> Erdos #32 (vf_2de03f410f195cdc) [related, confidence 0.55]: Both are additive-completeness problems asking that every sufficiently large integer be represented as a sum from a set (distinct elements in 123, p+a complements to primes in 32). -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.proposed
reason
SEMANTIC-EDGE DRAFT -> Erdos #32 (vf_2de03f410f195cdc) [related, confidence 0.55]: Both are additive-completeness problems asking that every sufficiently large integer be represented as a sum from a set (distinct elements in 123, p+a complements to primes in 32). -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
provenance
proposed by
agent:semantic-edge-extractor
actor type
human
created at
2026-06-10
target type
finding
affected
inspect finding →Erdős Problem #123 remains OPEN. Statement: **Erdős Problem #123** Let $a, b, c$ be three integers which are pairwise coprime. Is every large integer the sum of distinct integers of the form $a^k b^l c^m$ ($k, l, m ≥ 0$), none of which divide any other? Equivalently: is the set $\{a^k b^l c^m : k, l, m \geq 0\}$ d-complete? Note: For this not to reduce to the two-integer case, we need the integers to be greater than one and distinct. Topics: number theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
vf_9b39406ea761804fRead-only frontier; diff not recomputed.
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.
Jump to a section, signal, campaign, document, primitive, work path, frontier, record index, atlas, constellation, agent, capability, or full-state search.