TY - JOUR
T1 - On the number of distances between the coordinates of points on modular hyperbolas
AU - Shparlinski, Igor E.
AU - Winterhof, Arne
PY - 2008/5
Y1 - 2008/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=41149099607&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2007.04.016
DO - 10.1016/j.jnt.2007.04.016
M3 - Article
AN - SCOPUS:41149099607
SN - 0022-314X
VL - 128
SP - 1224
EP - 1230
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 5
ER -