Source labels openChecked July 26, 2026

Erdős Problem 445

Is it true that, for any $c>1/2$ , if $p$ is a sufficiently large prime then, for any $n\geq 0$ , there exist $a,b\in(n,n+p^c)$ such that $ab\equiv 1\pmod{p}$ ?

Number theory AMS 11

Mathematical statement

Is it true that, for any $c>1/2$ , if $p$ is a sufficiently large prime then, for any $n\geq 0$ , there exist $a,b\in(n,n+p^c)$ such that $ab\equiv 1\pmod{p}$ ?

This is discussed in this MathOverflow question [MathOverflow].

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_445

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_445 :    answer(sorry) ↔ ∀ c : ℝ, c > 1 / 2 →      ∀ᶠ p : ℕ in atTop, p.Prime → ∀ n : ℕ, Erdos445Prop c p 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 sourceformalization erdosproblems.com/445background MathOverflowbackground