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arXiv · 2608.27318

On Consecutive Non-primitive Elements over Finite Fields

Bidushi Sharma·Dhiren Kumar Basnet
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Abstract

In this article, we establish a bound on $\theta_q$ 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 $q-1$.

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Bidushi Sharma, Dhiren Kumar Basnet. 2026-08-27. On Consecutive Non-primitive Elements over Finite Fields. https://arxiv.org/abs/2608.27318

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