Rudin's conjecture on squares in arithmetic progressions
The strongest form of Rudin's conjecture also asserts uniqueness: for , any non-trivial arithmetic progression attaining the maximum has common difference . (Its initial term is then forced by ; the progression $24n + ...
Mathematical statement
The strongest form of Rudin's conjecture also asserts uniqueness: for , any non-trivial arithmetic progression attaining the maximum has common difference . (Its initial term is then forced by ; the progression is the canonical representative.)
Statement source: Wikipedia statement material
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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_unique
theorem rudins_conjecture_unique (N : ℕ) (hN : 6 ≤ N) (q a : ℕ) (hqa : IsNontrivial q a) (hmax : Q N q a = Qmax N) : q = 24 := 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