Quadratic non-residues and non-primitive roots satisfying a coprimality condition

2018/09/13 by Jaitra Chattopadhyay, Chattopadhyay, Jaitra, Bidisha Roy +5
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1809.04827

openalex publication_date 2018/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q≥ 1 be any integer and let ε∈ [(1)/(11), (1)/(2)) be a given real number. In this short note, we prove that for all primes p satisfying p≡ 1\pmodq, loglog p gt; (log 6.83)/((1)/(2)-ε) and (ϕ(p-1))/(p-1) ≤ (1)/(2) - ε, there exists a quadratic non-residue g which is not a primitive root modulo p such that gcd(g, (p-1)/(q)) = 1.

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