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: | , , , |
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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 http://irep.iium.edu.my/30701/ http://link.springer.com/article/10.1134%2FS0037446613030154 |
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| Institution: | Universiti Islam Antarabangsa Malaysia |
| Language: | English |
| Summary: | 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. |
|---|