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

• 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

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...