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WikipediaNumber theory

Rudin's conjecture on squares in arithmetic progressions

The strongest form of Rudin's conjecture also asserts uniqueness: for N6N \ge 6, any non-trivial arithmetic progression attaining the maximum Q(N)Q(N) has common difference 2424. (Its initial term is then forced by gcd(24,a)=1\gcd(24, a) = 1; the progression $24n + ...

Mathematical statement

The strongest form of Rudin's conjecture also asserts uniqueness: for N6N \ge 6, any non-trivial arithmetic progression attaining the maximum Q(N)Q(N) has common difference 2424. (Its initial term is then forced by gcd(24,a)=1\gcd(24, a) = 1; the progression 24n+124n + 1 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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem rudins_conjecture_unique (N : ) (hN : 6  N) (q a : )    (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