On the matrix equation Xn=B over finite fields
Let GF(q) denote the finite field of order q=pe with p odd and prime. Let M denote the ring of m×m matrices with entries in GF(q). In this paper, we consider the problem of determining the number N=N(n,m,B) of the n-th roots in M of a given matrix B∈M.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000663 |
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| _version_ | 1832550241432240128 |
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| author | Maria T. Acosta-De-Orozco Javier Gomez-Calderon |
| author_facet | Maria T. Acosta-De-Orozco Javier Gomez-Calderon |
| author_sort | Maria T. Acosta-De-Orozco |
| collection | DOAJ |
| description | Let GF(q) denote the finite field of order q=pe with p odd and prime. Let M
denote the ring of m×m matrices with entries in GF(q). In this paper, we consider the problem
of determining the number N=N(n,m,B) of the n-th roots in M of a given matrix B∈M. |
| format | Article |
| id | doaj-art-c80190b3625148d4b29f966fec69865d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c80190b3625148d4b29f966fec69865d2025-02-03T06:07:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116353954410.1155/S0161171293000663On the matrix equation Xn=B over finite fieldsMaria T. Acosta-De-Orozco0Javier Gomez-Calderon1Department of Mathematics, Southwest Texas State University, San Marcos 78666-4603, Texas , USADepartment of Mathematics, Southwest Texas State University, San Marcos 78666-4603, Texas , USALet GF(q) denote the finite field of order q=pe with p odd and prime. Let M denote the ring of m×m matrices with entries in GF(q). In this paper, we consider the problem of determining the number N=N(n,m,B) of the n-th roots in M of a given matrix B∈M.http://dx.doi.org/10.1155/S0161171293000663finite fields and matrix powers. |
| spellingShingle | Maria T. Acosta-De-Orozco Javier Gomez-Calderon On the matrix equation Xn=B over finite fields International Journal of Mathematics and Mathematical Sciences finite fields and matrix powers. |
| title | On the matrix equation Xn=B over finite fields |
| title_full | On the matrix equation Xn=B over finite fields |
| title_fullStr | On the matrix equation Xn=B over finite fields |
| title_full_unstemmed | On the matrix equation Xn=B over finite fields |
| title_short | On the matrix equation Xn=B over finite fields |
| title_sort | on the matrix equation xn b over finite fields |
| topic | finite fields and matrix powers. |
| url | http://dx.doi.org/10.1155/S0161171293000663 |
| work_keys_str_mv | AT mariatacostadeorozco onthematrixequationxnboverfinitefields AT javiergomezcalderon onthematrixequationxnboverfinitefields |