Turkish Journal of Mathematics
DOI
10.3906/mat-1803-14
Abstract
Suppose that $c$, $m$, and $a$ are positive integers with $a \equiv 11,\,13 \pmod{24}$. In this work, we prove that when $2c+1=a^{2}$, the Diophantine equation in the title has only solution $(x, y, z)=(1,1,2)$ where $m \equiv \pm 1 \pmod{a}$ and $m>a^2$ in positive integers. The main tools of the proofs are elementary methods and Baker's theory.
Keywords
Exponential Diophantine equation, Jacobi symbol, lower bound for linear forms in logarithms
First Page
2690
Last Page
2698
Recommended Citation
KIZILDERE, ELİF; MIYAZAKI, TAKAFUMI; and SOYDAN, GÖKHAN
(2018)
"On the Diophantine equation $((c+1)m^{2}+1)^{x}+(cm^{2}-1)^{y}=(am)^z$,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 45.
https://doi.org/10.3906/mat-1803-14
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/45
