Quadratic residues that are not primitive roots

2017/10/11 by Tamiru Jarso, Tim Trudgian, Jarso, Tamiru +1
Computer Science · Mathematics · #11A07 #11N35 #11N69 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1710.04320

openalex publication_date 2017/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any prime p satisfying ϕ(p-1)≤ (p-1)/4 contains two consecutive quadratic non-residues modulo p neither of which is a primitive root modulo p.

Citations

• Approximate formulas for some functions of prime numbers

Related

• Quadratic non-residues and non-primitive roots satisfying a coprimality condition
• Consecutive Quadratic Residues And Quadratic Nonresidue Modulo p
• Sums of Quadratic residues and nonresidues
• Least primitive root and simultaneous power-non residues
• On consecutive quadratic non-residues: a conjecture of Issai Schur