IMO 2020, Problem 2

The following is a question from IMO 2020: The first time I tried to solve the problem, I thought I had a solution, but it turned out to be wrong. I wrongly assumed that would be maximized when , which is commonly true in Olympiad problems, but that needn’t be the case. I then lookedContinue reading “IMO 2020, Problem 2”

A proof of Muirhead’s Inequality

I’ve been reading Thomas Mildorf’s Olympiad Inequalities, and trying to prove the 12 Theorems stated at the beginning. I’m recording my proof of Muirhead’s Inequality below. Although it is probably known to people working in this area, I could not find it on the internet. Muirhead’s Inequality states the following: if the sequence majorizes theContinue reading “A proof of Muirhead’s Inequality”