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Small residue classes with small reciprocal

Let $p$ be a large prime. For any $m \in \{1,\ldots,p-1\}$, let $\overline{m} \in \{1,\ldots,p-1\}$ be the reciprocal in ${\bf Z}/p{\bf Z}$ (i.e. the unique element of $\{1,\ldots …