Recently, Miyazaki and Togbé proved that for any fixed odd integer b ≥ 5 with b ≠ 89, the Diophantine equation has only the solution (x,y,z) = (1,1,1). We give an extension of this result.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-7,
author = {Min Tang and Quan-Hui Yang},
title = {The Diophantine equation $(bn)^{x} + (2n)^{y} = ((b+2)n)^{z}$
},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {95-100},
zbl = {06212151},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-7}
}
Min Tang; Quan-Hui Yang. The Diophantine equation $(bn)^{x} + (2n)^{y} = ((b+2)n)^{z}$
. Colloquium Mathematicae, Tome 131 (2013) pp. 95-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-7/