Sequences in power residue classes

Using A. Well's estimates the authors have given bounds for the largest prime P0 such that all primes p>P0 have sequences of quadratic residues of length m. For m≤8 the smallest prime having m consecutive quadratic residues is ≡3(mod4) and P0≡1(mod4). The reason for this phenomenon is invest...

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Main Authors:	Duncan A. Buell, Richard H. Hudson
Format:	Article
Language:	English
Published:	Hindawi Limited 1986-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	sequences of consecutive rth power residues random sequences of zeros and ones linear least squares fit.
Online Access:	http://dx.doi.org/10.1155/S0161171286000315

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spelling	doaj-30b9aa20faa6488a92baab7797cd88372020-11-24T22:05:38ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019226126610.1155/S0161171286000315Sequences in power residue classesDuncan A. Buell0Richard H. Hudson1Department of Computer Science, Louisiana State University, Baton Rouge 70803, LA, USADepartment of Mathematics, University of South Carolina, Columbia 29208, SC, USAUsing A. Well's estimates the authors have given bounds for the largest prime P0 such that all primes p>P0 have sequences of quadratic residues of length m. For m≤8 the smallest prime having m consecutive quadratic residues is ≡3(mod4) and P0≡1(mod4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for rth power residues, r≥2, r even.http://dx.doi.org/10.1155/S0161171286000315sequences of consecutive rth power residuesrandom sequences of zeros and oneslinear least squares fit.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Duncan A. Buell Richard H. Hudson
spellingShingle	Duncan A. Buell Richard H. Hudson Sequences in power residue classes International Journal of Mathematics and Mathematical Sciences sequences of consecutive rth power residues random sequences of zeros and ones linear least squares fit.
author_facet	Duncan A. Buell Richard H. Hudson
author_sort	Duncan A. Buell
title	Sequences in power residue classes
title_short	Sequences in power residue classes
title_full	Sequences in power residue classes
title_fullStr	Sequences in power residue classes
title_full_unstemmed	Sequences in power residue classes
title_sort	sequences in power residue classes
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1986-01-01
description	Using A. Well's estimates the authors have given bounds for the largest prime P0 such that all primes p>P0 have sequences of quadratic residues of length m. For m≤8 the smallest prime having m consecutive quadratic residues is ≡3(mod4) and P0≡1(mod4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for rth power residues, r≥2, r even.
topic	sequences of consecutive rth power residues random sequences of zeros and ones linear least squares fit.
url	http://dx.doi.org/10.1155/S0161171286000315
work_keys_str_mv	AT duncanabuell sequencesinpowerresidueclasses AT richardhhudson sequencesinpowerresidueclasses
_version_	1725825378340044800

Sequences in power residue classes

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