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arXiv · 2506.04087

Close points on a modular hyperbola

Tsz Ho Chan
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Abstract

In this paper, we continue the study of small squares containing at least two points on a modular hyperbola $x y \equiv c \pmod{p}$. We deduce a lower bound for its side length. We also investigate what happens if the ``distances" between two such points are special type of numbers like prime numbers, squarefree numbers or smooth numbers as well as more general multiplicatively closed sets or almost dense sets.

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Tsz Ho Chan. 2025-06-04. Close points on a modular hyperbola. https://arxiv.org/abs/2506.04087

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