Title: On the smallest simultaneous power nonresidue modulo a prime
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 $c_r\ge e^{-(1+o(1))r} \; (r\to \infty).$
Publication Year: 2015
Publication Date: 2015-11-26
Language: en
Type: preprint
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