Add to ORKGIn this paper, we find all the solutions of the title Diophantine equation in positive integer variables (m, n, x,y), where (P_k) is the kth term of the Pell sequence
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
AbstractUsing a theorem on linear forms in logarithms, we show that the equation px−2y=pu−2v has no ...
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
We study the exponential Diophantine equation $x^2+p^mq^n=2y^p$ in positive integers $x,y,m,n$, and ...
AbstractLet S be the set of all positive integers with prime divisors from a fixed finite set of pri...
In this paper, we first show that the exponential Diophantine equation 2x + 1 = z2has the unique sol...
Abstract. In this paper, we establish a number of theorems on the classic Diophantine equation of S....
We study solvability of the Diophantine equation in integers satisfying the conditions and for . The...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
AbstractUsing a theorem on linear forms in logarithms, we show that the equation px−2y=pu−2v has no ...
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
We study the exponential Diophantine equation $x^2+p^mq^n=2y^p$ in positive integers $x,y,m,n$, and ...
AbstractLet S be the set of all positive integers with prime divisors from a fixed finite set of pri...
In this paper, we first show that the exponential Diophantine equation 2x + 1 = z2has the unique sol...
Abstract. In this paper, we establish a number of theorems on the classic Diophantine equation of S....
We study solvability of the Diophantine equation in integers satisfying the conditions and for . The...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exp...
AbstractUsing a theorem on linear forms in logarithms, we show that the equation px−2y=pu−2v has no ...