Arithmetic progression in a finite field with prescribed norms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910289786568704 |
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| author | Chatterjee, Kaustav Sharma, Hariom Shukla, Aastha Tiwari, Shailesh Kumar |
| author_facet | Chatterjee, Kaustav Sharma, Hariom Shukla, Aastha Tiwari, Shailesh Kumar |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_01819 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic progression in a finite field with prescribed norms Chatterjee, Kaustav Sharma, Hariom Shukla, Aastha Tiwari, Shailesh Kumar Number Theory 12E20, 11T23 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. |
| title | Arithmetic progression in a finite field with prescribed norms |
| topic | Number Theory 12E20, 11T23 |
| url | https://arxiv.org/abs/2401.01819 |