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 statement2 of 4

Small example: for $p=5$ , $c=1$ , $n=0$ , the pair $(2,3) \in (0,5)$ satisfies $2 \cdot 3 = 6 \equiv 1 \pmod{5}$ .

FormalConjectures/ErdosProblems/445.leanErdos445.erdos_445.test.small_example1 lineExact file

1Erdos445.Erdos445Prop 1 5 1

TestStatement only, no proof