Distribution of Residues Modulo p

Gun, S. ; Luca, Florian ; Rath, P. ; Sahu, B. ; Thangadurai, R. (2007) Distribution of Residues Modulo p Acta Arithmetica, 129 (4). pp. 325-333. ISSN 0065-1036

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Related URL: http://dx.doi.org/10.4064/aa129-4-3


The distribution of quadratic residues and non-residues modulo p has been of intrigue to the number theorists of the last several decades. Although Gauss’ celebrated Quadratic Reciprocity Law gives a beautiful criterion to decide whether a given number is a quadratic residue modulo p or not, it is still an open problem to find a small upper bound on the least quadratic non-residue mod p as a function of p, at least when p ≡ 1 (mod 8). This is because for any given natural number N one can construct many primes p ≡ 1 (mod 8) having the first N positive integers as quadratic residue (see, for example, Theorem 3 below).

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematics Polish Academy of Sciences (IMPAN).
Keywords:Quadratic Residues; Primitive Roots; Finite Fields.
ID Code:117990
Deposited On:10 May 2021 12:45
Last Modified:10 May 2021 12:45

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