The time has come! My favorite subject and one of the most highly-requested topics: Proofathon Algebra. We've compiled a nice set of problems for you, so come on and stop by at proofathon.org, and while you're at it, support us on our Facebook page.
For those of you new to Proofathon, we have monthly Olympiad-level proof-based contests that are based on a certain topic each month. There are 8 problems ranging in difficulty from introductory to difficult. Hence, we encourage all to submit solutions to any problems you can do. Good luck, Proofathoners!