Modular hyperbolas and Beatty sequences

Marc Technau

Bounds for $\max \{m,\tilde{m}\}$ subject to $m,\tilde{m}\in \mathbb{Z}\cap [1,p)$, $p$ prime, $z$ indivisible by $p$, $m\tilde{m}\equiv z\mathrm{mod}p$ and $m$ belonging to some fixed Be…