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

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

445.lean

Retained formal statement3 of 4

Heath-Brown [He00] used Kloosterman sums to prove this for all $c>3/4$ .

FormalConjectures/ErdosProblems/445.leanErdos445.erdos_445.variants.heath_brown1 lineExact file

1∀ c > 3 / 4, ∀ᶠ (p : ℕ) in Filter.atTop, Nat.Prime p → ∀ (n : ℕ), Erdos445.Erdos445Prop c p n

SolvedStatement only, no proof