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Are quadratic residues random?

Are quadratic residues random? ISSN 1560-3547, Regular and Chaotic Dynamics, 2010, Vol. 15, Nos. 4–5, pp. 425–430.  c Pleiades Publishing, Ltd., 2010. Special Issue: Valery Vasilievich Kozlov–60 †* V. I. Arnol’d V. A. Steklov Mathematical Institute of RAS Gubkina str. 8, Moscow, 119991 Russia and Universit´ e Paris–Dauphine Place du Mare’chal de Lattre de Tassigny, Paris, 75775, France Received December 28, 2009 MSC2000 numbers: 11A07, 11N69 DOI: 10.1134/S1560354710040027 Key words: arithmetical dynamics, quadratic residue, randomness 1. STATISTICS OF DISTINCT QUADRATIC RESIDUES The set Z (the set of all n remainders in division by an integer number n, i.e., the finite circle of length n) contains the subset of k quadratic residues modulo n (i.e., remainders in division by n of all elements of the form x , x ∈ Z , of the ring Z ). n n Example. The number k of all (distinct) quadratic residues modulo n = 100 equals 22. These k points divide the finite circle of length n into k arcs with lengths a : a + a + ··· + a = n. 1 2 k In the previous example (n = 100, k = 22), the values a = m occur q(m)times, where the multiplicities http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Are quadratic residues random?

Arnol’d, V.
Regular and Chaotic Dynamics , Volume 15 (5) – Aug 6, 2010
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354710040027
Publisher site
See Article on Publisher Site

Abstract

ISSN 1560-3547, Regular and Chaotic Dynamics, 2010, Vol. 15, Nos. 4–5, pp. 425–430.  c Pleiades Publishing, Ltd., 2010. Special Issue: Valery Vasilievich Kozlov–60 †* V. I. Arnol’d V. A. Steklov Mathematical Institute of RAS Gubkina str. 8, Moscow, 119991 Russia and Universit´ e Paris–Dauphine Place du Mare’chal de Lattre de Tassigny, Paris, 75775, France Received December 28, 2009 MSC2000 numbers: 11A07, 11N69 DOI: 10.1134/S1560354710040027 Key words: arithmetical dynamics, quadratic residue, randomness 1. STATISTICS OF DISTINCT QUADRATIC RESIDUES The set Z (the set of all n remainders in division by an integer number n, i.e., the finite circle of length n) contains the subset of k quadratic residues modulo n (i.e., remainders in division by n of all elements of the form x , x ∈ Z , of the ring Z ). n n Example. The number k of all (distinct) quadratic residues modulo n = 100 equals 22. These k points divide the finite circle of length n into k arcs with lengths a : a + a + ··· + a = n. 1 2 k In the previous example (n = 100, k = 22), the values a = m occur q(m)times, where the multiplicities

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Regular and Chaotic Dynamics – Springer Journals

Published: Aug 6, 2010

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