Elements of high order in finite fields of the form

DOI10.1016/j.ffa.2012.01.003zbMath1251.11086OpenAlexW4205415370MaRDI QIDQ439074

Roman B. Popovych

Publication date: 1 August 2012

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2012.01.003

zbMATH Keywords

finite fieldsmultiplicative orderinteger partitionGauss period

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (12)

On the multiplicative order of the roots of \(bX^{q^r + 1} - aX^{q^r} + dX - c\) ⋮ Lower bounds on the orders of subgroups connected with Agrawal conjecture ⋮ High order elements in finite fields arising from recursive towers ⋮ On \(r\)-primitive \(k\)-normal elements over finite fields ⋮ Some primitive elements for the Artin-Schreier extensions of finite fields ⋮ LOWER BOUNDS FOR PERIODS OF DUCCI SEQUENCES ⋮ Elements of high order in Artin-Schreier extensions of finite fields \(\mathbb{F}_q\) ⋮ Subgroups generated by rational functions in finite fields ⋮ Sharpening of the explicit lower bounds for the order of elements in finite field extensions based on cyclotomic polynomials ⋮ Multiplicative orders of Gauss periods and the arithmetic of real quadratic fields ⋮ Unnamed Item ⋮ Elements of large order on varieties over prime finite fields

Cites Work

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• Finite field elements of high order arising from modular curves
• PRIMES is in P
• On the construction of finite field elements of large order
• MULTIPLICATIVE ORDER OF GAUSS PERIODS
• Elements of provable high orders in finite fields
• It is easy to determine whether a given integer is prime

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