Source labels openChecked July 26, 2026

Green's Open Problem 28

Suppose that $X, Y$ are two finitely-supported independent random variables taking integer values, and such that $X + Y$ is uniformly distributed on its range. Are $X$ and $Y$ themselves uniformly distributed on their ranges?

Probability AMS 60

Mathematical statement

Statement source: Green's Open Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

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

green_28

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_28 : answer(sorry) ↔  ∀ (X Y : PMF ℤ), -- marginals, independence is built into indepSum    X.support.Finite ∧ Y.support.Finite ∧ IsUniformOnSupport (indepSum X Y) →      IsUniformOnSupport X ∧ IsUniformOnSupport Y := 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 Green, Ben. "100 open problems." (2024).background Mathoverflow/339137background Silbackground