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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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 |
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International Islamic University Malaysia |
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language |
English |
topic |
QA Mathematics |
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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 |