Source labels openChecked July 26, 2026

Erdős Problem 257

Let $A\subseteq\mathbb{N}$ be an infinite set. Is $\sum_{n\in A} \frac{1}{2^n - 1}$ irrational?

Mathematical statement

Let $A\subseteq\mathbb{N}$ be an infinite set. Is

\sum_{n\in A} \frac{1}{2^n - 1}

irrational?

Statement source: Erdős 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

erdos_257

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_257 : answer(sorry) ↔ ∀ (A : Set ℕ), A.Infinite →    Irrational (∑' n : A, (1 : ℝ) / (2 ^ n.1 - 1)) := 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 erdosproblems.com/257background