Primitive Points on a Modular Hyperbola
Volume 54 / 2006
Bulletin Polish Acad. Sci. Math. 54 (2006), 193-200
MSC: 11A07, 11K38, 11L40.
DOI: 10.4064/ba54-3-1
Abstract
For positive integers $m$, $U$ and $V$, we obtain an asymptotic formula for the number of integer points $(u,v) \in [1, U]\times [1,V]$ which belong to the modular hyperbola $uv \equiv 1 \pmod m$ and also have $\gcd(u, v) =1$, which are also known as primitive points. Such points have a nice geometric interpretation as points on the modular hyperbola which are “visible” from the origin.
