Add to ORKGWe show that the Diophantine equation 2x+ 17y = z^2, has exactlyve solutions (x; y; z) in positive integers. The only solutions are (3; 1; 5), (5; 1; 7),(6; 1; 9), (7; 3; 71) and (9; 1; 23). This note, in turn, addresses an open problemproposed by Sroysang in [10].DOI : http://dx.doi.org/10.22342/jims.22.2.422.177-18
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...
AbstractWe show that the equations x10 + y10 = z2 and x10 - y10 = z2 have no nontrivial integral sol...
In this short note, we study some Diophantine equations of the form px+qy = z2, where x,y, and z are...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
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 $x \ge 1$, $y >1$,...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the dioph...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
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...
AbstractWe show that the equations x10 + y10 = z2 and x10 - y10 = z2 have no nontrivial integral sol...
In this short note, we study some Diophantine equations of the form px+qy = z2, where x,y, and z are...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
AbstractIn this paper, we prove the equation in the title has no positive integer solutions (x,y,n) ...
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 $x \ge 1$, $y >1$,...
In this paper, we show that the Diophantine equation 3 x + 5 y = z 2 has a unique non-negative integ...
We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < ...
AbstractWe sharpen work of Bugeaud to show that the equation of the title has, for t = 1 or 2, no so...
In this short note, we shall give a result similar to Y. Zhang and T. Cai [5] which states the dioph...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
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...
AbstractWe show that the equations x10 + y10 = z2 and x10 - y10 = z2 have no nontrivial integral sol...