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Quadratic Non-Residues Versus Primitive Roots Modulo p
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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.
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