OP-7004Status unassessedNumber theory

Zhi-Wei Sun's 2-4-6-8 Conjecture

TheoremDB P9090 · Candidate awaiting source review

Inferred from the community field; finer classification has not been reviewed.

Source candidate · not reviewedAs of 2026-09-08Source & evidence ↓

Read original source ↗ 0 Submit progress Lean 4 ↓Discussion (0)

Problem statement

For every positive integer $n$ , there exist nonnegative integers $w$ , $x$ , $y$ , and $z$ such that

n = \binom{w+2}{2} + \binom{x+3}{4} + \binom{y+5}{6} + \binom{z+7}{8}.

Prove that this representation always exists.

Lean 4

No Lean submitted

Formal statement

Lean 4

theorem conjecture (n : ℕ) (hn : 0 < n) : A n

Formalization source ↗

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A source attachment or link is not a verified proof. The statement’s correspondence with the original question needs human review.

Proofs & verification

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

This record is in the source backlog; its novelty and unresolved status have not passed source review.

References

[1]TheoremDB P9090 link
[2]Source formal statement (not locally verified) link

Recorded progress

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Machine attempts

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Discussion

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