An upper bound for the number of solutions of the exponential diophantine equation $a^x + b^y = c^z$
Le, Maohua
Proc. Japan Acad. Ser. A Math. Sci., Tome 75 (1999) no. 10, p. 90-91 / Harvested from Project Euclid
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Let $a$, $b$, $c$ be coprime positive integers which are power free. In this paper we prove that if $2\nmid c$, then the equation $a^x + b^y = c^z$ has at most $2^{\omega(c)+1}$ positive integer solutions $(x,y,z)$, where $\omega(c)$ is the number of distinct prime factors of $c$. Moreover, all solutions $(x,y,z)$ satisfy $z < 2ab \log(2eab) / \pi$.
Publié le : 1999-06-14
Classification:  Exponential diophantine equation,  the number of solutions,  upper bound,  11D61 
@article{1148393909,
     author = {Le, Maohua},
     title = {An upper bound for the number of solutions of the exponential diophantine equation $a^x + b^y = c^z$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {75},
     number = {10},
     year = {1999},
     pages = { 90-91},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148393909}
}

Le, Maohua. An upper bound for the number of solutions of the exponential diophantine equation $a^x + b^y = c^z$. Proc. Japan Acad. Ser. A Math. Sci., Tome 75 (1999) no. 10, pp.  90-91. http://gdmltest.u-ga.fr/item/1148393909/