We give a criterion for the existence of solutions to an equation of the form x 3 + ax = b, where a, b ∈ ℚp, in p-adic integers for p > 3. Moreover, in the case when the equation x 3 + 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.
|Number of pages||16|
|Journal||Siberian Mathematical Journal|
|Publication status||Published - May 2013|
- cubic equation
- p-adic number
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