Source labels openChecked July 26, 2026

Sum of a triangular number, a generalized pentagonal number, and a generalized heptagonal number

*Zhi-Wei Sun's Conjecture (A287616)**: Any nonnegative integer can be written as the sum of a triangular number $x(x+1)/2$ , a generalized pentagonal number $y(3y+1)/2$ , and a generalized heptagonal number $z(5z+1)/2$ , where $x, y, z$ are nonnegative integers.

Number theory AMS 11

Mathematical statement

Statement source: OEIS 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

conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem conjecture (n : ℕ) : A 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 A287616background