On the number of distances between the coordinates of points on modular hyperbolas

Igor E. Shparlinski*, Arne Winterhof

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

For a prime p > 2, an integer a with gcd (a, p) = 1 and 1 ≤ X, Y < p we give an asymptotic formula for the number of different Euclidean distances | x - y | defined by the points on the modular hyperbola {(x, y) : x y ≡ a (mod p), 1 ≤ x ≤ X, 1 ≤ y ≤ Y}. Furthermore, in the case X = Y = p - 1 we determine the exact number of different distances.

Original languageEnglish
Pages (from-to)1224-1230
Number of pages7
JournalJournal of Number Theory
Volume128
Issue number5
DOIs
Publication statusPublished - May 2008

Fingerprint Dive into the research topics of 'On the number of distances between the coordinates of points on modular hyperbolas'. Together they form a unique fingerprint.

Cite this