In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any natural number q. As an application of the result, we describe a relationship between q and p in which the number −1 is the q-th power of some p-adic number
AbstractWe extend the notion of monomial extensions of differential fields, i.e. simple transcendent...
We consider the diophantine equation xp - x = yq - y, in integers (x, p, y, q). We prove that for gi...
This paper deals with some fundamental questions in the study of the diagonal diophan-tine equation ...
AbstractIn this paper we provide a solvability criterion for the monomial equation xq=a over Qp for ...
We establish the solvability criteria for the equation xq=a in the field of p-adic numbers, for any ...
In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth o...
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a,...
Unlike real numbers, in general, the cubic equation is not necessary to have a solution over p-adic ...
In this paper, we introduce a square root function over the p-adic field Qp. This enables to explici...
AbstractKummer's method of proof is applied to the Fermat equation over quadratic fields. The concep...
AbstractThe solvability of the equation a1a2 … ak = x2, a1, a2, …, ak ϵ A is studied for fixed k and...
AbstractIn the work The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, George Andrews ga...
In the work The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, George Andrews gave a pro...
Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic numb...
Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational funct...
AbstractWe extend the notion of monomial extensions of differential fields, i.e. simple transcendent...
We consider the diophantine equation xp - x = yq - y, in integers (x, p, y, q). We prove that for gi...
This paper deals with some fundamental questions in the study of the diagonal diophan-tine equation ...
AbstractIn this paper we provide a solvability criterion for the monomial equation xq=a over Qp for ...
We establish the solvability criteria for the equation xq=a in the field of p-adic numbers, for any ...
In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth o...
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a,...
Unlike real numbers, in general, the cubic equation is not necessary to have a solution over p-adic ...
In this paper, we introduce a square root function over the p-adic field Qp. This enables to explici...
AbstractKummer's method of proof is applied to the Fermat equation over quadratic fields. The concep...
AbstractThe solvability of the equation a1a2 … ak = x2, a1, a2, …, ak ϵ A is studied for fixed k and...
AbstractIn the work The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, George Andrews ga...
In the work The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, George Andrews gave a pro...
Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic numb...
Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational funct...
AbstractWe extend the notion of monomial extensions of differential fields, i.e. simple transcendent...
We consider the diophantine equation xp - x = yq - y, in integers (x, p, y, q). We prove that for gi...
This paper deals with some fundamental questions in the study of the diagonal diophan-tine equation ...
DOI
Add to ORKG