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 $ab\equiv 1\pmod{p}$ ?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

FormalConjectures/ErdosProblems/445.lean

Formal Conjectures

FormalConjectures/ErdosProblems/445.leanErdos445.erdos_4451 lineExact file

1True ↔ ∀ c > 1 / 2, ∀ᶠ (p : ℕ) in Filter.atTop, Nat.Prime p → ∀ (n : ℕ), Erdos445.Erdos445Prop c p n

OpenStatement only, no proof