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Erdős ProblemsCombinatorics

Erdős Problem 358: One Le

It is conjectured that if A={a1<⋯ }A =\{a_1 < \cdots\} and gg counts the number of representations n=∑u≤i≤vain=\sum_{u\leq i\leq v}a_i such that the sum has at least two terms, then for all nn we have 1≤g(n)1 \leq g(n) for sufficiently large nn.

CombinatoricsAMS 5AMS 11

Mathematical statement

It is conjectured that if A={a1<⋯ }A =\{a_1 < \cdots\} and gg counts the number of representations n=∑u≤i≤vain=\sum_{u\leq i\leq v}a_i such that the sum has at least two terms, then for all nn we have 1≤g(n)1 \leq g(n) for sufficiently large nn.

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_358.variants.one_le

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_358.variants.one_le :    ∃ A, StrictMono A ∧ ∀ᶠ n in atTop, 1 ≤ g 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 sourceformalizationerdosproblems.com/358backgroundErdős problem 358background