Hey. First off, you don't prove that for instance, if you're working in Z_p then (p-1)+1=0, right? So, what you want to do is assume that you can't add 1 to its self a bunch of times and end up with 0. Then, show that the first time, the number of summands is prime. Then, you've covered all cases since either it's allways different than zero or it's not.