Document Type

Article

Publication Date

3-15-2023

Journal / Book Title

Acta Mathematica Sinica Chinese Series

Abstract

Consider any prime number p. In this paper, we use analytic methods, properties of Legendre’s symbol modulo p, and estimation for character sums to study distribution properties of triples of consecutive quadratic residues (named 3-CQR) and consecutive quadratic non-residues (3-CQN) modulo p. We provide exact formulas for the numbers S1(p) and S2(p) of 3-CQRs and 3-CQNs when p ≡ 3 or 7 (mod 8). Asymptotic formulas are given for p ≡ 1 or 5 (mod 8). Similarly, triples of quadratic residues with equal distance 2 are investigated and corresponding enumeration formulas are given. As an application, we further apply 3-CQRs to construct magic squares of squares of full degree over Fp

Comments

Article published in Chinese, no English translation available

DOI

10.12386/A20210160

Published Citation

Wang Xiao, Li Aihua. Distribution properties and applications of continuous quadratic residues. Acta Mathematica Sinica, 2023, 66(2): 389-398 https://doi.org/10.12386/A20210160

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