# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Primitive Points on a Modular Hyperbola

### Tom 54 / 2006

Bulletin Polish Acad. Sci. Math. 54 (2006), 193-200 MSC: 11A07, 11K38, 11L40. DOI: 10.4064/ba54-3-1

#### Streszczenie

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.

#### Autorzy

• Igor E. ShparlinskiDepartment of Computing
Macquarie University
Sydney, NSW 2109, Australia
e-mail

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