On the multiplicative order of elements in Wiedemann's towers of finite fields
We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} )$.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vasyl Stefanyk Precarpathian National University
2015-12-01
|
| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1401 |
| id |
doaj-cf4e5770e2cf4e56a3d72954d2a10671 |
|---|---|
| record_format |
Article |
| spelling |
doaj-cf4e5770e2cf4e56a3d72954d2a106712020-11-25T03:56:21ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102015-12-017222022510.15330/cmp.7.2.220-2251401On the multiplicative order of elements in Wiedemann's towers of finite fieldsR. Popovych0Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, UkraineWe consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} )$.https://journals.pnu.edu.ua/index.php/cmp/article/view/1401finite fieldmultiplicative orderwiedemann's tower |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
R. Popovych |
| spellingShingle |
R. Popovych On the multiplicative order of elements in Wiedemann's towers of finite fields Karpatsʹkì Matematičnì Publìkacìï finite field multiplicative order wiedemann's tower |
| author_facet |
R. Popovych |
| author_sort |
R. Popovych |
| title |
On the multiplicative order of elements in Wiedemann's towers of finite fields |
| title_short |
On the multiplicative order of elements in Wiedemann's towers of finite fields |
| title_full |
On the multiplicative order of elements in Wiedemann's towers of finite fields |
| title_fullStr |
On the multiplicative order of elements in Wiedemann's towers of finite fields |
| title_full_unstemmed |
On the multiplicative order of elements in Wiedemann's towers of finite fields |
| title_sort |
on the multiplicative order of elements in wiedemann's towers of finite fields |
| publisher |
Vasyl Stefanyk Precarpathian National University |
| series |
Karpatsʹkì Matematičnì Publìkacìï |
| issn |
2075-9827 2313-0210 |
| publishDate |
2015-12-01 |
| description |
We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} )$. |
| topic |
finite field multiplicative order wiedemann's tower |
| url |
https://journals.pnu.edu.ua/index.php/cmp/article/view/1401 |
| work_keys_str_mv |
AT rpopovych onthemultiplicativeorderofelementsinwiedemannstowersoffinitefields |
| _version_ |
1724465458403344384 |