Mathematical Notes

, Volume 73, Issue 3–4, pp 562–570

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

• V. E. Tarakanov
Article

## 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 $$\user2{(}\tfrac{\user1{a}}{\user1{p}}\user2{) = 1}$$ for each p from a given finite set M.

pseudorandom sequences Gauss lemma quadratic residues Jacobi symbol arithmetic progression

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