数学
组合数学
上下界
残留物(化学)
除数(代数几何)
主电源
最大公约数
离散数学
素数(序理论)
化学
数学分析
生物化学
标识
DOI:10.1016/j.jnt.2014.10.019
摘要
Let p be a prime number and let k≥2 be a divisor of p−1. Norton proved that the least k-th power non-residue mod p is at most 3.9p1/4logp unless k=2 and p≡3(mod4), in which case the bound is 4.7p1/4logp. By improving the upper bound in the Burgess inequality via a combinatorial idea, and by using some computing power, we improve the upper bounds to 0.9p1/4logp and 1.1p1/4logp, respectively.
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