1. The problem statement, all variables and given/known data If F is a finite field show that there is a prime p s.t. (p times)a+a+...+a=0 for all a in the field 2. Relevant equations 3. The attempt at a solution Well I managed to prove that there must be an a in F s.t. (prime number, call p, times)a+a+...+a=0 but I can't seem to prove that for every a in F (p times)a+a+...+a=0 (This is the only approach I could think of).