Close points on a modular hyperbola
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912413082714112 |
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| author | Chan, Tsz Ho |
| author_facet | Chan, Tsz Ho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Close points on a modular hyperbola Chan, Tsz Ho Number Theory 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. |
| title | Close points on a modular hyperbola |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.04087 |