Problem with my PROMYS application

Hey guys I’m very interested in going to PROMYS this summer I love math and it’s killer on your resume if I’m not mistaken. My problem is that I have no clue where to start in writing my proofs. It’s not that I can’t solve the problems or am turned off from all that work, it’s just I literally don’t know how to write non-geometry proofs and I couldn’t find anything helpful on the internet. Could anyone point me to resources on the internet / maybe pm me their old proofs so I can look at it and get an idea how to do it?