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Erdős·erdos:154

Erdős Problem 154

problem formal record: solved source: proved (Lean) F2 declared

No independent check recorded yet. A formal artifact, declaration or published object is attached, but no rebuild of it is recorded here.

Fidelity F2: The correspondence is declared through a Comparator challenge, an alignment table and written divergences.

sidon sets·Source

AI activity

How grades work
Aristotle, GPT

6 Feb 2026·supporting task

Lindström (1998)

full A1 V1 F2
Reasoning and sources

Autonomy

Secondary contribution: formalization

Details

proof to formalize: Lindström (1998)

Fidelity

How fidelity is graded

F2 declared. The correspondence is declared through a Comparator challenge, an alignment table and written divergences.

declares divergences from its source reviewed by its authors only

Declared by the projects

1

As each project's formalization.yaml states it.

lean-proofs: formal Lean 4 proofs of solved Erdős problemswillblair0708/lean-proofs · joined by artifact · no independent check

Read formalization.yaml

authors
Will Blair
method
agent
review
self-assessed
axioms
Classical.choice, Quot.sound, propext
sorry
0 unproved goals declared
results
3 main results named, checked with Comparator, with an alignment table
sources
Erdős Problem #730 (erdosproblems.com), after P. Erdős, R. L. Graham, I. Z. Ruzsa and E. G. Straus, 'On the prime factors of C(2n, n)', Math. Comp. 29 (1975) — background, authors n/a; Comment on Erdős Problem #730 asserting, with a one-paragraph gist, that GPT Pro proves infinitely many consecutive pairs (n, n+1) — formalizes, authors not-contacted; Closing derivation ('Proof Route Mapping') linked as a follow-up, reproducing the algebraic skeleton of the argument; the analytic sections exist only in a private document and are reconstructed in this formalisation — adapts, authors not-contacted; Bernt Lindström, 'Well distribution of Sidon sets in residue classes', J. Number Theory 69 (1998), 197–200 — adapts, authors n/a
related
Woett/Lean-files/blob/main/ErdosProblem154.lean — builds-on; AlexKontorovich/PrimeNumberTheoremAnd — builds-on; google-deepmind/formal-conjectures/pull/664 — other
divergences
#730: none in the statement — the Challenge inlines the Formal Conjectures set verbatim; the proof establishes the stronger consecutive-pair statement, available in the development as Erdos730.FullDensityCore.GoodParameter and the density theorems around it. #154: the Challenge states the sumset form Formal Conjectures records, which is the consequence proved here of Lindström's theorem for A itself, with IsSidon in the Formal Conjectures shape (two representations agree up to order). #94: an elementary bounded identity only; it does not prove the cubic distance-multiplicity theorem or the regular-polygon conjecture of that problem.
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Formal material

Formal statements · 1
Cited proofs · 2
Also known as · 3
  • https://www.erdosproblems.com/154
  • https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/154.lean
  • FormalConjectures/ErdosProblems/154.lean

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qed.bot, “Erdős Problem 154”, https://qed.bot/s/erdos-154, as of 30 Sep 2026.

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