OP-7003Status unassessedNumber theory

Zhi-Wei Sun's 1680-Conjecture on Refinements of Lagrange's Four-Square Theorem

TheoremDB P8922 · Candidate awaiting source review

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

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

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Problem statement

For every nonnegative integer $n$ , does there exist nonnegative integers $x$ , $y$ , $z$ , and $w$ such that $n = x^2 + y^2 + z^2 + w^2$ and $x^4 + 1680 y^3 z$ is a perfect square?

Lean 4

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Formal statement

Lean 4

theorem conjecture (n : ℕ) : A n

Formalization source ↗

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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 P8922 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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