Exploring Indian Mathematical Olympiads

Indian math olympiad questions are famous (infamous?) for being very analytical. There mostly do not exist any clever one line proofs. Multiple cases have to be analyzed and exhaustively eliminated before arriving upon the correct answer. I tried solving problems from the Indian National Mathematics Olympiad, 2013 today. My solutions are different (lengthier, and henceContinue reading “Exploring Indian Mathematical Olympiads”

A beautiful generalization of the Nesbitt Inequality

I want to discuss a beautiful inequality, that is a generalization of the famous Nesbitt inequality: (Romanian TST) For positive , prove that Clearly, if , then we get Nesbitt’s inequality, which states that . This is question 14 on Mildorf’s “Olympiad Inequalities”, and its solution comprises finding a factor to multiply this expression with,Continue reading “A beautiful generalization of the Nesbitt Inequality”

A small note on re-defining variables to prove inequalities

I just want to record my solution to the following problem, as it is different from the one given online. For positive real numbers, prove that This has a fairly straight forward solution using Cauchy-Schwarz inequality, which for some reason I did not think of. The way that I solved it is that I re-definedContinue reading “A small note on re-defining variables to prove inequalities”