It seems so easy... I can't believe there's no simple proof for this one! :/
There is only one known elementary proof, at least, I think. It came from Euler, but it is a mess, many texts omit his proof but only mention it.
A sufficent (but not necessary) condition to determine whether you will be the next great mathemation can be determined if you can solve diophantine equations. If yes, then you have no need to fear.