Geodesic
Primitive Points on a Modular Hyperbola
Igor E. Shparlinski1
1Department of Computing Macquarie University Sydney, NSW 2109, Australia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 3, pp. 193-200

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DOI

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.
DOI : 10.4064/ba54-3-1
Keywords: positive integers obtain asymptotic formula number integer points times which belong modular hyperbola equiv pmod have gcd which known primitive points points have nice geometric interpretation points modular hyperbola which visible origin

Igor E. Shparlinski  1

1 Department of Computing Macquarie University Sydney, NSW 2109, Australia 
Igor E. Shparlinski. Primitive Points on a Modular Hyperbola. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 3, pp. 193-200. doi: 10.4064/ba54-3-1
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