Originally Posted by

**kimberu** My problem is to show that $\displaystyle m^3+14n^3-12=0$ 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 $\displaystyle Z_3$ or $\displaystyle Z_5$. 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!