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arXiv · 1511.08428

On the smallest simultaneous power nonresidue modulo a prime

Kevin Ford·Moubariz Garaev·Sergei Konyagin
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Abstract

Let $p$ be a prime and $p_1,\ldots, p_r$ be distinct prime divisors of $p-1$. We prove that the smallest positive integer $n$ which is a simultaneous $p_1,\ldots,p_r$-power nonresidue modulo $p$ satisfies $$ n<p^{1/4 - c_r+o(1)}\quad(p\to\infty) $$ for some positive $c_r$ satisfying $c_r\ge e^{-(1+o(1))r} \; (r\to \infty).$

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Kevin Ford, Moubariz Garaev, Sergei Konyagin. 2015-11-26. On the smallest simultaneous power nonresidue modulo a prime. https://arxiv.org/abs/1511.08428

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