Turkish Journal of Mathematics
DOI
10.3906/mat-1905-20
Abstract
Let $a,\ m$ be positive integers such that $am\not\equiv0\pmod{3}, 2\nmid a$, and $a>3$. We prove that the exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$ has only the positive integer solution $(x,y,z)=(1,1,2)$.
Keywords
Diophantine equation, positive integer solution, Fibonacci number
First Page
2561
Last Page
2567
Recommended Citation
DENG, NAI-JUAN; WU, DAN-YAO; and YUAN, PING-ZHI
(2019)
"The exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 39.
https://doi.org/10.3906/mat-1905-20
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/39
