My problem is to show that has no solution in the integers.

I've done other problems like this with one variable, where you show that there are no roots in, say or . However with this equation I know Z2, Z3, Z4, Z6 won't work and I've found roots in Z5 and Z7 already. Do I need to go even higher or am I missing something obvious? Does anyone know which Zx I should try, if I do indeed need to go higher?

Thanks a lot!