On plain lattice points whose coordinates are reciprocals modulo a prime
We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to condition xy ≡ 1 (mod p) and with radius r. We are concerned with the size of r.
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| Published in | Nagoya mathematical journal Vol. 147; pp. 137 - 146 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.09.1997
Nagoya University 名古屋大学 Duke University Press |
| Subjects | |
| Online Access | Get full text |
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| Abstract | We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to condition xy ≡ 1 (mod p) and with radius r. We are concerned with the size of r. |
|---|---|
| AbstractList | We consider, for a given large prime
p
, the problem of covering a square [0,
p
] × [0,
p
] with discs center at the lattice point (
x, y
),
x
and
y
subject to condition
xy
≡ 1 (mod
p
) and with radius
r
. We are concerned with the size of
r
. We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to condition xy ≡ 1 (mod p) and with radius r. We are concerned with the size of r. |
| Author | Kitaoka, Yoshiyuki Fujii, Akio |
| Author_xml | – sequence: 1 givenname: Akio surname: Fujii fullname: Fujii, Akio email: fujii@rkmath.rikkyo.ac.jp organization: Department of Mathematics, Rikkyo University, Toshima-ku, Tokyo 171, Japan, fujii@rkmath.rikkyo.ac.jp – sequence: 2 givenname: Yoshiyuki surname: Kitaoka fullname: Kitaoka, Yoshiyuki email: kitaokaOmath.nagoya-u.ac.jp organization: Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan, kitaokaOmath.nagoya-u.ac.jp |
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| Cites_doi | 10.1007/BF01077956 10.3792/pjaa.68.198 |
| ContentType | Journal Article |
| Copyright | Copyright © Editorial Board of Nagoya Mathematical Journal 1997 Copyright 1997 Editorial Board, Nagoya Mathematical Journal |
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| DocumentTitleAlternate | A. FUJII AND Y. KITAOKA LATTICE POINTS (X, Y) WITH XY = 1(P) |
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| Snippet | We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to... We consider, for a given large prime p , the problem of covering a square [0, p ] × [0, p ] with discs center at the lattice point ( x, y ), x and y subject to... |
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| Title | On plain lattice points whose coordinates are reciprocals modulo a prime |
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