On the difference between a D. H. Lehmer number and its inverse over short interval

Yana Niu, Rong Ma, Haodong Wang

Let $q>2$ be an odd integer. For each integer $x$ with $0<x<q$ and $(q,x)=1$, we know that there exists one and only one $\bar{x}$ with $0<\bar{x}<q$ such that $x\bar{x}\equiv1(\b…