A note on the diophantine equation $x^2+b^Y=c^z$

Title:

A note on the diophantine equation $x^2+b^Y=c^z$

Creator:

Le, Maohua

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0c38799a-b00b-42ac-b361-dd5fbb76afee
uuid:0c38799a-b00b-42ac-b361-dd5fbb76afee

Subject:

exponential diophantine equation, Lucas number, and positive divisor

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $a$, $b$, $c$, $r$ be positive integers such that $a^{2}+b^{2}=c^{r}$, $\min (a,b,c,r)>1$, $\gcd (a,b)=1, a$ is even and $r$ is odd. In this paper we prove that if $b\equiv 3\hspace{4.44443pt}(\@mod \; 4)$ and either $b$ or $c$ is an odd prime power, then the equation $x^{2}+b^{y}=c^{z}$ has only the positive integer solution $(x,y,z)=(a,2,r)$ with $\min (y,z)>1$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1109-1116

Source:

Czechoslovak Mathematical Journal | 2006 Volume:56 | Number:4

Harvested from:

CDK

Metadata only:

false