1. The problem statement, all variables and given/known data Suppose a finite group has exactly n elements of order p where p is prime. Prove that either n=0 or p divides n + 1. 2. Relevant equations My professor says that this proof is similiar to the proof of Lagrange's Theorem, in our Abstract Algebra book (Gallian). 3. The attempt at a solution I am so lost with this question. It is a "special problem" we've been given to work on all semester. I have tried letting H represent a subgroup of the finite group, and using the elements of order p in the original group to form left cosets of H in the group. Not sure I really understand that. Not sure where that is getting me. I am not used to feeling so lost when tackling a problem. Please...can anyone steer me in the right direction? Thank you!