Add to ORKGWe establish the solvability criteria for the equation xq=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 shown that solvability problem of xq=a for any q can be reduced to the cases (i) and (ii)
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
Consider a system of polynomial equations in n variables of degrees less than d with integer coeffic...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...
AbstractIn this paper we provide a solvability criterion for the monomial equation xq=a over Qp for ...
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a,...
In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth o...
Unlike real numbers, in general, the cubic equation is not necessary to have a solution over p-adic ...
Solvability criteria for cubic equations over the p-adic field, where p>3, were studied in previous ...
Solvability criteria for cubic equations over the p-adic field, where p>3, were studied in previous ...
In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any n...
Este texto é sobre solubilidade no corpo dos p-ádicos de sistemas de duas formas aditivas: com grau...
We provide a solvability criterion for a cubic equation in domains . We show that, in principal, the...
Este trabalho é baseado nos artigos de Atkinson, Brüdern e Cook [2] e I. D. Meir [15] que tratam de ...
This paper deals with some fundamental questions in the study of the diagonal diophan-tine equation ...
The p-adic models of statistical mechanics require the investigation of the roots of polynomial equa...
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
Consider a system of polynomial equations in n variables of degrees less than d with integer coeffic...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...
AbstractIn this paper we provide a solvability criterion for the monomial equation xq=a over Qp for ...
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a,...
In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth o...
Unlike real numbers, in general, the cubic equation is not necessary to have a solution over p-adic ...
Solvability criteria for cubic equations over the p-adic field, where p>3, were studied in previous ...
Solvability criteria for cubic equations over the p-adic field, where p>3, were studied in previous ...
In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any n...
Este texto é sobre solubilidade no corpo dos p-ádicos de sistemas de duas formas aditivas: com grau...
We provide a solvability criterion for a cubic equation in domains . We show that, in principal, the...
Este trabalho é baseado nos artigos de Atkinson, Brüdern e Cook [2] e I. D. Meir [15] que tratam de ...
This paper deals with some fundamental questions in the study of the diagonal diophan-tine equation ...
The p-adic models of statistical mechanics require the investigation of the roots of polynomial equa...
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
Consider a system of polynomial equations in n variables of degrees less than d with integer coeffic...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...