R. Popovych

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math.NT2025

High order elements in extensions of finite fields given by binomials

Roman Popovych

We construct explicitly in any finite field of the form Fq[x]/(x^m-a) elements with multiplicative order at least 2^{(2m)^(1/2)}

math.NT2022

Elements of high order in finite fields specified by binomials

Victor Bovdi, Adama Diene, Roman Popovych

Let $F_{q}$ be a field with $q$ elements, where $q$ is a power of a prime number $p \geq 5$ . For any integer $m \geq 2$ and $a \in F_{q}^{*}$ such that the polynomial $x^{m} - a$ is irreducible…