For reference: I am a 10th grader, and I predict a 720 770 on the 2025 USAMO, which gives me a score of 23, or a 22 if something goes wrong (see below).

Notes:

1. I don't know if I am getting any partials on Problem 2. My work has everything up until and including using PHP and getting two consecutive coefficients equal to 0. I am giving myself 2 points here based on what others have said.

2. My Problem 5 solution has a few writing errors in one section (specifically I forgot an exponent of k in two equations but fixed it later on in the writeup). Hopefully I don't get docked here.