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Solvability Criteria for the Equation $X^q=a$ in the Field of $P$-adic Numbers by Casas, J. M.; Omirov, B. A.; Rozikov, U. A. is a scholarly article available to read on EtoBox.

What is Solvability Criteria for the Equation $X^q=a$ in the Field of $P$-adic Numbers about?

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 criteria we show that any $p$-adic number can be represented in finitely many different forms and we describe the algorithms to obtain the corresponding representations. Moreover it is showed that solvability problem of $x^q=a$ for any $q$ can be reduced to the cases (i) and (ii).

Author

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

Published

2011

Language

EN