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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

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

Bibliographic databases:

Document Type: Article
UDC: 511.37
Received: 07.07.2002

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
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