Primitive Points on a Modular Hyperbola

Igor E. Shparlinski. "Primitive Points on a Modular Hyperbola." Bulletin of the Polish Academy of Sciences. Mathematics 54.3 (2006): 193-200. <http://eudml.org/doc/280580>.

@article{IgorE2006,
abstract = {For positive integers m, U and V, we obtain an asymptotic formula for the number of integer points (u,v) ∈ [1,U] × [1,V] which belong to the modular hyperbola uv ≡ 1 (mod 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.},
author = {Igor E. Shparlinski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {modular hyperbola; primitive point},
language = {eng},
number = {3},
pages = {193-200},
title = {Primitive Points on a Modular Hyperbola},
url = {http://eudml.org/doc/280580},
volume = {54},
year = {2006},
}

TY - JOUR
AU - Igor E. Shparlinski
TI - Primitive Points on a Modular Hyperbola
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2006
VL - 54
IS - 3
SP - 193
EP - 200
AB - For positive integers m, U and V, we obtain an asymptotic formula for the number of integer points (u,v) ∈ [1,U] × [1,V] which belong to the modular hyperbola uv ≡ 1 (mod 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.
LA - eng
KW - modular hyperbola; primitive point
UR - http://eudml.org/doc/280580
ER -