Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3153
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 $(x,y,z)=(1,1,2)$.
Keywords
Ternary purely exponential Diophantine equation, application of the Baker method
First Page
1224
Last Page
1232
Recommended Citation
FUJITA, YASUTSUGU and LE, MAOHUA
(2022)
"A parametric family of ternary purely exponential Diophantine equation $A^x+B^y=C^z$,"
Turkish Journal of Mathematics: Vol. 46:
No.
4, Article 6.
https://doi.org/10.55730/1300-0098.3153
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss4/6
