Does the equation $x^3+y^5=z^7$ have a solution $(x,y,z)$ with $x,y,z$ positive integers and $(x,y)=1$? In his book H. Cohen (Number theory,2007) said "[...] seems presently out of reach". I couldn't find any suggestion beyond Cohen's book. Thanks in advance,

Montanari Fabio department of math university of bologna italy e-mail [email protected]