有限域上的连续非本原元
On Consecutive Non-primitive Elements over Finite Fields
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中文总结 AI 辅助
该研究针对有限域F_q，通过特征和推导充分条件，结合q-1的最小素因子分情况讨论，建立θ_q的界，保证除q=4、q=8外存在连续非本原元对。
中文摘要 AI 辅助
本文中，我们建立了θ_q的一个界，该界保证在有限域F_q中存在一对连续非本原元，例外情况为q=4和q=8。我们首先利用特征和推导了这类元素对存在的充分条件，随后根据q-1的最小素因子分多种情况讨论，得到了上述界。
英文摘要
In this article, we establish a bound on $θ_q$ that guarantees the existence of a pair of consecutive non-primitive elements in $\mathbb{F}_q$, with the exceptions $q=4$ and $q=8$. We first derive a sufficient condition for the existence of such a pair using character sums and then obtain the stated bound by considering several cases according to the least prime divisor of $q-1$.
