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

Abstract

In this paper we provide a solvability criterion for the monomial equation $x^q=a$ over $Q_p$ for any natural number $q$.

5 pages

References in corpus (2)

• Solvability criteria for the equation $x^q=a$ in the field of $p$-adic numbers
• On cubic equations over $P-$adic field

Cited by in corpus (7)

• Phase transitions for $P$-adic Potts model on the Cayley tree of order three
• $P$-adic monomial equations and their perturbation
• On $P$-adic Ising-Vannimenus model on an arbitrary order Cayley tree
• Solvability criteria for the equation $x^q=a$ in the field of $p$-adic numbers
• On cubic equations over $P-$adic field
• The Dynamics of The Potts-Bethe Mapping over ${\mathbb{Q}}_p:$ The Case $p\equiv 2(mod3)$
• On the coefficient-choosing game