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 a^ab^bc^cd^d would be maximized when a=b=c=d, which is commonly true in Olympiad problems, but that needn’t be the case.

I then looked at solutions available online, and realized that I just needed to show that a^ab^bc^cd^d\leq a^2+b^2+c^2+d^2. After doing that, I homogenized both sides, and tried to prove the statement. I was finally successful. I am recording my solution, as it is slightly different from the ones available online.


Published by ayushkhaitan3437

Hello! My name is Ayush Khaitan, and I'm a graduate student in Mathematics. I am always excited about talking to people about their research. Please please set up a meeting with me if you feel that I might have an interesting perspective to offer- https://calendly.com/ayushkhaitan/meeting-with-ayush

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