Solvability of cubic equations in p-adic integers (p > 3) - Mukhamedov, Farrukh; Omirov, Bakhrom; Saburov, Mansoor; Masutova, Kamilyam (Springer Science+Business Media, Inc., 2013)
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.