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pro vyhledávání: '"Kapetanakis, Giorgos"'
Let $r$ be a positive divisor of $q-1$ and $f(x,y)$ a rational function of degree sum $d$ over $\mathbb{F}_q$ with some restrictions, where the degree sum of a rational function $f(x,y) = f_1(x,y)/f_2(x,y)$ is the sum of the degrees of $f_1(x,y)$ and
Externí odkaz:
http://arxiv.org/abs/2410.03836
Autor:
Kapetanakis, Giorgos, Rizos, Ioannis
Let $a,b$ be positive, relatively prime, integers. Our goal is to characterize, in an elementary way, all positive integers $c$ that can be expressed as a linear combination of $a,b$ with non-negative integer coefficients and discuss the teaching per
Externí odkaz:
http://arxiv.org/abs/2308.03173
Autor:
Kapetanakis, Giorgos, Rizos, Ioannis
Let $a,b$ be positive, relatively prime, integers. We prove, using induction, that for every $d > ab-a-b$ there exist $x,y\in\mathbb{Z}_{\geq 0}$, such that $d=ax+by$.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2308.03050
Let $q, n, m \in \mathbb{N}$ such that $q$ is a prime power, $m \geq 3$ and $a \in \mathbb{F}$. We establish a sufficient condition for the existence of a primitive normal pair ($\alpha$, $f(\alpha)$) in $\mathbb{F}_{q^m}$ over $\mathbb{F}_{q}$ such
Externí odkaz:
http://arxiv.org/abs/2306.03426
By definition primitive and $2$-primitive elements of a finite field extension $\mathbb{F}_{q^n}$ have order $q^n-1$ and $(q^n-1)/2$, respectively. We have already shown that, with minor reservations, there exists a primitive element and a $2$-primit
Externí odkaz:
http://arxiv.org/abs/2108.08066
Let $\mathcal C_Q$ be the cyclic group of order $Q$, $n$ a divisor of $Q$ and $r$ a divisor of $Q/n$. We introduce the set of $(r,n)$-free elements of $\mathcal C_Q$ and derive a lower bound for the the number of elements $\theta \in \mathbb F_q$ for
Externí odkaz:
http://arxiv.org/abs/2108.07373
Autor:
Cohen, Stephen D. Stephen.Cohen@glasgow.ac.uk, Kapetanakis, Giorgos1 gnkapet@gmail.com
Publikováno v:
Southeast Asian Bulletin of Mathematics. 2024, Vol. 48 Issue 2, p161-184. 24p.
On existence of primitive normal elements of rational form over finite fields of even characteristic
Let $q$ be an even prime power and $m\geq2$ an integer. By $\mathbb{F}_q$, we denote the finite field of order $q$ and by $\mathbb{F}_{q^m}$ its extension degree $m$. In this paper we investigate the existence of a primitive normal pair $(\alpha, \,
Externí odkaz:
http://arxiv.org/abs/2005.01216
Let $r,n>1$ be integers and $q$ be any prime power $q$ such that $r\mid q^n-1$. We say that the extension $\mathbb{F}_{q^n}/\mathbb{F}_q$ possesses the line property for $r$-primitive elements if, for every $\alpha,\theta\in\mathbb{F}_{q^n}^*$, such
Externí odkaz:
http://arxiv.org/abs/1910.10061
Let $r,n>1$ be integers and $q$ be any prime power $q$ such that $r\mid q^n-1$. We say that the extension $\mathbb{F}_{q^n}/\mathbb{F}_q$ possesses the line property for $r$-primitive elements property if, for every $\alpha,\theta\in\mathbb{F}_{q^n}^
Externí odkaz:
http://arxiv.org/abs/1906.08046