Source labels openChecked July 26, 2026

Rudin's conjecture on squares in arithmetic progressions

Rudin's conjecture.* The maximal number of squares among the first $N$ terms of a non-trivial arithmetic progression grows at most like $\sqrt{N}$ : $Q(N) = O(\sqrt{N}).$

Number theory AMS 11

Mathematical statement

Rudin's conjecture.* The maximal number of squares among the first $N$ terms of a non-trivial arithmetic progression grows at most like $\sqrt{N}$ : $Q(N) = O(\sqrt{N}).$

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

rudins_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem rudins_conjecture :    (fun N : ℕ => (Qmax N : ℝ)) =O[atTop] fun N : ℕ => Real.sqrt N := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipediabackground