3=-1 mod 4
so we're back to
the only solution to this is
so x=4x', y=4y', z=4z', for some integers x', y', z' different from 0
thus the equation is
divide by 256 and you'll get the initial equation again.
this is the method of infinite ascent (if I'm not mistaking), similar to Fermat's infinite descent, and this means that there is no other solution than (0,0,0)