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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/30701/1/mf-SMJ%282013%29.pdf
http://irep.iium.edu.my/30701/
http://link.springer.com/article/10.1134%2FS0037446613030154
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spelling my.iium.irep.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 REM 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
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
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/30701/1/mf-SMJ%282013%29.pdf
http://irep.iium.edu.my/30701/
http://link.springer.com/article/10.1134%2FS0037446613030154
_version_ 1643609922523365376
score 13.244404

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