Source labels openChecked July 26, 2026

Erdős Problem 945: Constant

Is there a constant $C > 0$ such that, for all large $x$ , every interval $[x, x+(\log x)C]$ contains two integers with the same number of divisors?

Number theory AMS 11

Mathematical statement

Is there a constant $C > 0$ such that, for all large $x$ , every interval $[x, x+(\log x)C]$ contains two integers with the same number of divisors?

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_945.variants.constant

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_945.variants.constant : answer(sorry) ↔ Erdos945Constant := 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/945background