Let a,b,c be fixed coprime positive integers with mina,b,c > 1, and let m = maxa,b,c. Using the Gel’fond-Baker method, we prove that all positive integer solutions (x,y,z) of the equation satisfy maxx,y,z < 155000(log m)³. Moreover, using that result, we prove that if a,b,c satisfy certain divisibility conditions and m is large enough, then the equation has at most one solution (x,y,z) with minx,y,z > 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-2-4,
author = {Yongzhong Hu and Maohua Le},
title = {A note on ternary purely exponential diophantine equations},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {173-182},
zbl = {06497307},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-2-4}
}
Yongzhong Hu; Maohua Le. A note on ternary purely exponential diophantine equations. Acta Arithmetica, Tome 168 (2015) pp. 173-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-2-4/