Solvability criteria for the equation $x^q=a$ in the field of $p$-adic numbers

J. M. Casas, B. A. Omirov, U. A. Rozikov

We establish the solvability criteria for the equation $x^q=a$ in the field of $p$-adic numbers, for any $q$ in two cases: (i) $q$ is not divisible by $p$; (ii) $q=p$. Using these…