Solvability of cubic equations in p-adic integers (p > 3)
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a, b ∈ Qp, in p-adic integers for p > 3. Moreover, in the case when the equation x3 + ax = b is solvable, we give necessary and sufficient recurrent conditions on a p-adic number x ∈ Z ∗ p under w...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer Science+Business Media, Inc.
2013
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/30701/1/mf-SMJ%282013%29.pdf |
| _version_ | 1825647357935484928 |
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| author | Mukhamedov, Farrukh Omirov, Bakhrom Saburov, Mansoor Masutova, Kamilyam |
| author_facet | Mukhamedov, Farrukh Omirov, Bakhrom Saburov, Mansoor Masutova, Kamilyam |
| author_sort | Mukhamedov, Farrukh |
| collection | IIUM |
| description | We give a criterion for the existence of solutions to an equation of the form x3 + ax = b,
where a, b ∈ Qp, in p-adic integers for p > 3. Moreover, in the case when the equation x3 + ax = b is
solvable, we give necessary and sufficient recurrent conditions on a p-adic number x ∈ Z
∗
p under which
x is a solution to the equation. |
| first_indexed | 2024-03-05T23:16:25Z |
| format | Article |
| id | oai:generic.eprints.org:30701 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:16:25Z |
| publishDate | 2013 |
| publisher | Springer Science+Business Media, Inc. |
| record_format | dspace |
| spelling | oai:generic.eprints.org:307012013-08-05T02:22:58Z http://irep.iium.edu.my/30701/ Solvability of cubic equations in p-adic integers (p > 3) Mukhamedov, Farrukh Omirov, Bakhrom Saburov, Mansoor Masutova, Kamilyam QA Mathematics We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a, b ∈ Qp, in p-adic integers for p > 3. Moreover, in the case when the equation x3 + ax = b is solvable, we give necessary and sufficient recurrent conditions on a p-adic number x ∈ Z ∗ p under which x is a solution to the equation. Springer Science+Business Media, Inc. 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/30701/1/mf-SMJ%282013%29.pdf Mukhamedov, Farrukh and Omirov, Bakhrom and Saburov, Mansoor and Masutova, Kamilyam (2013) Solvability of cubic equations in p-adic integers (p > 3). Siberian Mathematical Journal, 54 (3). pp. 501-516. ISSN 1573-9260 (O), 0037-4466 (P) http://link.springer.com/article/10.1134%2FS0037446613030154 10.1134/S0037446613030154 |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Omirov, Bakhrom Saburov, Mansoor Masutova, Kamilyam Solvability of cubic equations in p-adic integers (p > 3) |
| title | Solvability of cubic equations in p-adic integers (p > 3) |
| title_full | Solvability of cubic equations in p-adic integers (p > 3) |
| title_fullStr | Solvability of cubic equations in p-adic integers (p > 3) |
| title_full_unstemmed | Solvability of cubic equations in p-adic integers (p > 3) |
| title_short | Solvability of cubic equations in p-adic integers (p > 3) |
| title_sort | solvability of cubic equations in p adic integers p 3 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/30701/1/mf-SMJ%282013%29.pdf |
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