Does the equation x^3+y^5=z^7 has 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]