Geodesic
$p$-adic monomial equations and their perturbations
Izvestiya. Mathematics , Tome 84 (2020) no. 2, pp. 348-360

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In this paper, we describe the set of solutions of the monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, as an application, we study some perturbations of the equation under consideration over the $p$-adic field.
Keywords: $p$-adic numbers, rational function.
Mots-clés : monomial equation 
@article{IM2_2020_84_2_a5,
     author = {F. M. Mukhamedov and O. N. Khakimov},
     title = {$p$-adic monomial equations and their perturbations},
     journal = {Izvestiya. Mathematics },
     pages = {348--360},
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     volume = {84},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a5/}
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F. M. Mukhamedov; O. N. Khakimov. $p$-adic monomial equations and their perturbations. Izvestiya. Mathematics , Tome 84 (2020) no. 2, pp. 348-360. http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a5/