Turkish Journal of Mathematics
Abstract
Let $a,b,c$ be fixed positive integers such that $a+b=c^2$, $2 \nmid c$ and $(b/p)\ne 1$ for every prime divisor $p$ of $c$, where $(b/p)$ is the Legendre symbol. Further let $m$ be a positive integer with $m>1$. In this paper, using the Baker method, we prove that if $m>\max\{10^8,c^2\}$, then the equation $(am^2+1)^x+(bm^2-1)^y=(cm)^z$ has only one positive integer solution $(x,y,z)=(1,1,2)$.
DOI
10.55730/1300-0098.3153
Keywords
Ternary purely exponential Diophantine equation, application of the Baker method
First Page
1224
Last Page
1232
Recommended Citation
FUJITA, Y, & LE, M (2022). A parametric family of ternary purely exponential Diophantine equation $A^x+B^y=C^z$. Turkish Journal of Mathematics 46 (4): 1224-1232. https://doi.org/10.55730/1300-0098.3153
