An upper bound for the number of solutions of the exponential diophantine equation \(a^x+b^y=c^z\) (Q1125417)

In this paper, the author proves that if \(2\nmid c\) then the equation \(a^x+b^y=c^z\) has at most \(2^{\omega (c)+1}\) solutions \((x,y,z)\in {\mathbb N}\), and all solutions \((x,y,z)\in {\mathbb N}\) satisfy \(z<2ab \log(2eab)/{\pi}\), where \(\omega (c)\) is the number of distinct prime factors of \(c\). The reviewer notes that the result is implied from a paper of the reviewer [On the diophantine equation \(ax^2+by^2=p^z\), J. Harbin Inst. Tech. 23, No. 6, 108-111 (1991)].