Geometric properties of points on modular hyperbolas

Kevin Ford*, Mizan R. Khan, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
3 Downloads (Pure)


Given an integer n ≥ 2, let Hn be the set Hn = {(a, b) : ab ≡1 (modn), 1 ≤ a, b ≤ n - 1} and let M(n) be the maximal difference of b-a for (a, b) ∈ Hn. We prove that for almost all n, n-M(n) = O (n1/2+o(1)). We also improve some previously known upper and lower bounds on the number of vertices of the convex closure of Hn.

Original languageEnglish
Pages (from-to)4177-4185
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number12
Publication statusPublished - Dec 2010

Bibliographical note

Copyright [2010] American Mathematical Society. First published in Proceedings of the American Mathematical Society, 138:12, pp. 4177-4185, published by the American Mathematical Society. The original article can be found at


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