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arXiv · 2401.01819

Arithmetic progression in a finite field with prescribed norms

Kaustav Chatterjee·Hariom Sharma·Aastha Shukla·Shailesh Kumar Tiwari
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Abstract

Given a prime power $q$ and a positive integer $n$, let $\mathbb{F}_{q^{n}}$ represents a finite extension of degree $n$ of the finite field ${\mathbb{F}_{q}}$. In this article, we investigate the existence of $m$ elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for $n\geq6,q=3^k,m=2$ we establish that there are only $10$ possible exceptions.

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Kaustav Chatterjee, Hariom Sharma, Aastha Shukla, Shailesh Kumar Tiwari. 2024-01-03. Arithmetic progression in a finite field with prescribed norms. https://arxiv.org/abs/2401.01819

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