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Source labels openChecked July 26, 2026

WikipediaNumber theory

Sum of three cubes

An integer n : ℤ can be written as a sum of three cubes (of integers) if and only if n is not 4 or 5 mod 9.

Mathematical statement

An integer n : ℤ can be written as a sum of three cubes (of integers) if and only if n is not 4 or 5 mod 9.

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

isSumOfThreeCubes_iff_mod_9

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem isSumOfThreeCubes_iff_mod_9 :    answer(sorry)   n : , IsSumOfThreeCubes n  ¬(n ≡ 4 [ZMOD 9]  n ≡ 5 [ZMOD 9]) := 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