On equation $x^q=a$ over $\bq_p$

Details On equation $x^q=a$ over $\bq_p$ On equation $x^q=a$ over $\bq_p$

2011-06-29

arxiv.org/abs/1106.5935v1

Mathematics

Number Theory

10 pages

Scientific paper

In this paper we provide a solvability criteria for the equation $x^q=a$ over
$\bq_p$ for any natural number $q$. We fix some mistakes in the proofs of the
results given in arXiv:1102.2156 and generalize those results. As an
application of our results, we describe a relationship between $q$ and $p$ in
which the number -1 is the $q$-th power of some $p-$adic number.

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