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]