Solvability of cubic equations in p-adic integers (p > 3)

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...

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Main Authors: Mukhamedov, Farrukh, Omirov, Bakhrom, Saburov, Mansoor, Masutova, Kamilyam
Format: Article
Language:English
Published: Springer Science+Business Media, Inc. 2013
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/30701/
http://irep.iium.edu.my/30701/
http://irep.iium.edu.my/30701/
http://irep.iium.edu.my/30701/1/mf-SMJ%282013%29.pdf
id iium-30701
recordtype eprints
spelling iium-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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
Omirov, Bakhrom
Saburov, Mansoor
Masutova, Kamilyam
Solvability of cubic equations in p-adic integers (p > 3)
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.
format Article
author Mukhamedov, Farrukh
Omirov, Bakhrom
Saburov, Mansoor
Masutova, Kamilyam
author_facet Mukhamedov, Farrukh
Omirov, Bakhrom
Saburov, Mansoor
Masutova, Kamilyam
author_sort Mukhamedov, Farrukh
title Solvability of cubic equations in p-adic integers (p > 3)
title_short 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_sort solvability of cubic equations in p-adic integers (p > 3)
publisher Springer Science+Business Media, Inc.
publishDate 2013
url http://irep.iium.edu.my/30701/
http://irep.iium.edu.my/30701/
http://irep.iium.edu.my/30701/
http://irep.iium.edu.my/30701/1/mf-SMJ%282013%29.pdf
first_indexed 2023-09-18T20:44:55Z
last_indexed 2023-09-18T20:44:55Z
_version_ 1777409610497392640

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