Solvability of cubic equations in p-ADIC integers (p > 3)
Farrukh MukhamedovInternational Islamic University Malaysia, Kuantan, Pahang, MalaysiaB. A. OmirovInstitute of Mathematics at the National University of Uzbekistan, Tashkent, UzbekistanMansoor SaburovInternational Islamic University Malaysia, Kuantan, Pahang, MalaysiaK. K. MasutovaInstitute of Mathematics at the National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Abstract
We give a criterion for the existence of solutions to an equation of the form x 3 + ax = b, where a, b ∈ ℚ p , 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.
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