For approximately the last two years, I have been working off and on for a proof of whether Brocard's problem was finite and what it's solutions were. Brocard's problem refers to the question as to whether the following equation, n!+1=m2 possesses a finite number of solutions; specifically anymore than n=4, 5, and 7. The following attachment is my final proof. If you all see any problems with it please inform me. If you have any trouble following the logic, please ask to elaborate or give a better potential wording. Any help would be extremely appreciated as I would like this proof to be as strong as possible.