RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2003, Volume 73, Issue 4, Pages 603–612 (Mi mz208)

An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues

V. E. Tarakanov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In the context of the study of pseudorandom sequences that use quadratic residues modulo the prime $p$, the constructive description of the set of prime moduli for which given integers are quadratic residues is considered. Using the Gauss Lemma, we prove a criterion of combinatorial nature for a given integer $a$ to be a quadratic residue prime modulo $p$. It is shown how to apply this criterion to the problem of effective description of the prime moduli $p$ satisfying the equation $(\frac ap)=1$ for each $p$ from a given finite set $M$.

DOI: https://doi.org/10.4213/mzm208

Full text: PDF file (190 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2003, 73:4, 562–570

Bibliographic databases:

Document Type: Article
UDC: 511.37

Citation: V. E. Tarakanov, “An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues”, Mat. Zametki, 73:4 (2003), 603–612; Math. Notes, 73:4 (2003), 562–570

Citation in format AMSBIB
\Bibitem{Tar03} \by V.~E.~Tarakanov \paper An Application of the Gauss Lemma to the Study of Pseudorandom Sequences Based on Quadratic Residues \jour Mat. Zametki \yr 2003 \vol 73 \issue 4 \pages 603--612 \mathnet{http://mi.mathnet.ru/mz208} \crossref{https://doi.org/10.4213/mzm208} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1991906} \zmath{https://zbmath.org/?q=an:1101.11004} \transl \jour Math. Notes \yr 2003 \vol 73 \issue 4 \pages 562--570 \crossref{https://doi.org/10.1023/A:1023267406766} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182776700032} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0347124817}