The Diophantine equation $(bn)^{x}+(2n)^{y}=((b+2)n)^{z}$
Volume 132 / 2013
Colloquium Mathematicum 132 (2013), 95-100
MSC: Primary 11D61.
DOI: 10.4064/cm132-1-7
Abstract
Recently, Miyazaki and Togbé proved that for any fixed odd integer $b\geq 5$ with $b\not =89$, the Diophantine equation $b^{x}+2^{y}=(b+2)^{z}$ has only the solution $(x,y,z)=(1,1,1)$. We give an extension of this result.
