We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for the case when xab is odd. Our main result is Theorem 1
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
summary:Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$,...
summary:Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$,...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
We study the exponential Diophantine equation $x^2+p^mq^n=2y^p$ in positive integers $x,y,m,n$, and ...
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
AbstractThe title equation, where p>3 is a prime number ≢7(mod8), q is an odd prime number and x, y,...
In this paper, we find all the solutions of the title Diophantine equation in positive integer varia...
Suppose that $U_n$ is a Lucas sequence of first kind and has a dominant root $\alpha$ with $\alpha>1...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
summary:Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$,...
summary:Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$,...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
We study the exponential Diophantine equation $x^2+p^mq^n=2y^p$ in positive integers $x,y,m,n$, and ...
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
AbstractThe title equation, where p>3 is a prime number ≢7(mod8), q is an odd prime number and x, y,...
In this paper, we find all the solutions of the title Diophantine equation in positive integer varia...
Suppose that $U_n$ is a Lucas sequence of first kind and has a dominant root $\alpha$ with $\alpha>1...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
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