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Scholz conjecture on addition chains

The Scholz conjecture, also known as the Scholz-Brauer conjecture, asserts that for every positive integer $n$ , the addition-chain length of $2^n - 1$ is at most $n - 1 + \ell(n)$ .

Number theory AMS 11 AMS 68

Mathematical statement

The Scholz conjecture, also known as the Scholz-Brauer conjecture, asserts that for every positive integer $n$ , the addition-chain length of $2^n - 1$ is at most $n - 1 + \ell(n)$ .

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

scholz_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem scholz_conjecture :    answer(sorry) ↔ ∀ (n : ℕ), 0 < n → ℓ(2 ^ n - 1) ≤ n - 1 + ℓ(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 MathWorldbackground Tall22background