Roman Popovych

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 2, Pages 47—52

DOI: 10.7546/nntdm.2020.26.2.47-52

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## Details

### Authors and affiliations

Roman Popovych

*Department of Specialized Computer Systems, Lviv Polytechnic National University
Bandery Str.,12, Lviv, 79013, Ukraine
*

### Abstract

We obtain explicit lower bound on multiplicative orders of all elements in finite field extensions generated by a root of unity. The bound does not depend on any unknown constant. The result of Ahmadi, Shparlinski and Voloch [1] is a consequence of our main result.

### Keywords

- Finite field
- Multiplicative order
- Lower bound
- Partition

### 2010 Mathematics Subject Classification

- 11T30

### References

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Popovych, R. (2013). Elements of high order in finite fields of the form*F*[_{q}*x*] / (*x*−^{m}*a*), Finite Fields Appl., 19 (1), 86–92. - Voloch, J. F. (2007). On the order of points on curves over finite fields, Integers, 7, A49.
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## Cite this paper

Popovych, R. (2020). On multiplicative order of elements in finite fields based on cyclotomic polynomials. Notes on Number Theory and Discrete Mathematics, 26 (2), 47-52, doi: 10.7546/nntdm.2020.26.2.47-52.