Tamiru Jarso, Tim Trudgian
Abstract
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We prove that any prime p p satisfying ϕ ( p − 1 ) ≤ ( p − 1 ) / 4 \phi (p-1)\leq (p-1)/4 contains two consecutive quadratic non-residues modulo p p neither of which is a primitive root modulo p p . This improves on results by Luca et al. and Gun et al.
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We prove that any prime p p satisfying ϕ ( p − 1 ) ≤ ( p − 1 ) / 4 \phi (p-1)\leq (p-1)/4 contains two consecutive quadratic non-residues modulo p p neither of which is a primitive root modulo p p . This improves on results by Luca et al. and Gun et al.
Key concepts: Modulo, Primitive root modulo n, Mathematics, Quadratic residue, Quadratic equation, Prime (order theory), Combinatorics, Root (linguistics)