Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Quadratic Non-Residues Versus Primitive Roots Modulo p


Affiliations
1 Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, C.P. 58089, Morelia, Michoacan, Mexico
2 Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
3 Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
     

   Subscribe/Renew Journal


Given any ε ∈ (0, 1/2) and any positive integer s ≥ 2, we prove that for every prime

p ≥ max{s2(4/ε)2s, s651s log log(10s)} 

satisfying ϕ(p − 1)/(p − 1) ≤ 1/2 − ε, where ϕ(k) is the Euler function, there are s consecutive quadratic non-residues which are not primitive ischolar_mains modulo p.


User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 222

PDF Views: 0




  • Quadratic Non-Residues Versus Primitive Roots Modulo p

Abstract Views: 222  |  PDF Views: 0

Authors

Florian Luca
Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, C.P. 58089, Morelia, Michoacan, Mexico
Igor E. Shparlinski
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
R. Thangadurai
Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India

Abstract


Given any ε ∈ (0, 1/2) and any positive integer s ≥ 2, we prove that for every prime

p ≥ max{s2(4/ε)2s, s651s log log(10s)} 

satisfying ϕ(p − 1)/(p − 1) ≤ 1/2 − ε, where ϕ(k) is the Euler function, there are s consecutive quadratic non-residues which are not primitive ischolar_mains modulo p.