On multiplicative order of elements in finite fields based on cyclotomic polynomials

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
Full paper (PDF, 97 Kb)

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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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