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OEISNumber theory

The 2-4-6-8 Conjecture

*Zhi-Wei Sun's 2-4-6-8 Conjecture (A306477)**: Any integer n>0n > 0 can be written as (w+22)+(x+34)+(y+56)+(z+78)\binom{w+2}{2} + \binom{x+3}{4} + \binom{y+5}{6} + \binom{z+7}{8} for nonnegative integers w,x,y,zw, x, y, z.

Number theoryAMS 11

Mathematical statement

*Zhi-Wei Sun's 2-4-6-8 Conjecture (A306477)**: Any integer n>0n > 0 can be written as (w+22)+(x+34)+(y+56)+(z+78)\binom{w+2}{2} + \binom{x+3}{4} + \binom{y+5}{6} + \binom{z+7}{8} for nonnegative integers w,x,y,zw, x, y, z.

Statement source: OEIS statement material

Statement terms: CC-BY-SA-4.0

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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) (hn : 0 < 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 sourceformalizationA306477backgroundmathoverflow/323541background