Source labels openChecked July 26, 2026

Taxicab numbers

Taxicab number for $k=5$ and $m=2$ is not-known for any $n ≥ 2$ . Whether such a number exists is also not known.

Number theory AMS 11

Mathematical statement

Taxicab number for $k=5$ and $m=2$ is not-known for any $n ≥ 2$ . Whether such a number exists is also not known.

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

taxicab_for_5_2_n

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem taxicab_for_5_2_n : answer(sorry) ↔ ∃ n : ℕ, n ≥ 2 ∧ (∃ x : ℕ, IsTaxicabFor 5 2 n x)  := 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 Generalized taxicab numberbackground OEIS taxicab cubesbackground