Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1803-14
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
