Source labels openChecked July 26, 2026

Erdős Problem 357: Infinite Set Sum

Suppose $A$ is an infinite set such that all finite sums of consecutive terms of $A$ are distinct. Then it is conjectured that the sum $\sum_k \frac{1}{a_k}$ converges.

Number theory AMS 11

Mathematical statement

Suppose $A$ is an infinite set such that all finite sums of consecutive terms of $A$ are distinct. Then it is conjectured that the sum $\sum_k \frac{1}{a_k}$ converges.

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_357.variants.infinite_set_sum

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_357.variants.infinite_set_sum (A : ℕ → ℕ) (hA : StrictMono A)    (hA : HasDistinctSums A) :    Summable (fun i ↦ (1 : ℝ) / A i) := 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/357background