Tamiru Jarso, Tim Trudgian
Abstract
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We prove that any prime $p$ satisfying $ϕ(p-1)\leq (p-1)/4$ contains two consecutive quadratic non-residues modulo $p$ neither of which is a primitive root modulo $p$.
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We prove that any prime $p$ satisfying $ϕ(p-1)\leq (p-1)/4$ contains two consecutive quadratic non-residues modulo $p$ neither of which is a primitive root modulo $p$.
Key concepts: Modulo, Primitive root modulo n, Quadratic residue, Quadratic equation, Prime (order theory), Mathematics, Root (linguistics), Combinatorics