Add to ORKGLet a, b, c be fixed coprime positive integers with min(a,b,c)>1. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions (x,y,z) of the ternary purely exponential diophantine equation ax + by = cz
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
AbstractIn 1956 L. Jeśmanowicz conjectured, for any primitive Pythagorean triple (a,b,c) satisfying ...
Let (A) $B$ be positive integers such that $min{A,B}>1$, $gcd(A,B) = 1$ and $2|B.$ In this paper, us...
Let (A) $B$ be positive integers such that $min{A,B}>1$, $gcd(A,B) = 1$ and $2|B.$ In this paper, us...
Let b and c be fixed coprime odd positive integers with min{b,c}>1. In this paper, a classification ...
Abstract. In this paper, we establish a number of theorems on the classic Diophantine equation of S....
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...
Let r be a positive integer with r > 1, and let m be a positive even integer. Further let a = |V ...
Abstract. We prove a generalization of an old conjecture of Pillai (now a theorem of Stroeker and Ti...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
Click on the link to view the abstract.Keywords: Exponential Diophantine equation, Terai conjecture,...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In ...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
AbstractIn 1956 L. Jeśmanowicz conjectured, for any primitive Pythagorean triple (a,b,c) satisfying ...
Let (A) $B$ be positive integers such that $min{A,B}>1$, $gcd(A,B) = 1$ and $2|B.$ In this paper, us...
Let (A) $B$ be positive integers such that $min{A,B}>1$, $gcd(A,B) = 1$ and $2|B.$ In this paper, us...
Let b and c be fixed coprime odd positive integers with min{b,c}>1. In this paper, a classification ...
Abstract. In this paper, we establish a number of theorems on the classic Diophantine equation of S....
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...
Let r be a positive integer with r > 1, and let m be a positive even integer. Further let a = |V ...
Abstract. We prove a generalization of an old conjecture of Pillai (now a theorem of Stroeker and Ti...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
Click on the link to view the abstract.Keywords: Exponential Diophantine equation, Terai conjecture,...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In ...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
AbstractIn 1956 L. Jeśmanowicz conjectured, for any primitive Pythagorean triple (a,b,c) satisfying ...