Let $ϵ>0$. Does there exist a constant $C_{ϵ}$ such that, for all primes $p$, every residue modulo $p$ is the sum of at most $C_{ϵ}$ many elements of$$\{n^{-1}:1\le n\le p^{ϵ}\}$$where $n^{-1}$ denotes the inverse of $n$ modulo $p$?