Assume there is a solution to the equation. Then if you take the mod n of both sides the new equality will also hold, for any n. Therefore, if you can prove th

Assume there is a solution to the equation. Then if you take the mod n of both sides the new equality will also hold, for any n. Therefore, if you can prove there are no solution for the mod n equation, then the original equation is also not solvable. This of course also hold when n is prime.