Just wanted to record a cute combinatorial argument. Prove that I read this formula in the article “Pascal functions” in “The American Mathematical Monthly”. They prove it using the new machinery of Pascal functions that they develop in the article. I tried proving it using an algebraic argument, but couldn’t find the rightContinue reading “A cute combinatorial identity”
I solved two math problems today. The solutions to both were uniquely disappointing. The first problem was the first problem from IMO 1986: Let be a number that is not or . Prove that out of the set , we can select two different numbers such that is not a square. A quick check wouldContinue reading “Some solutions”
Here’s a slightly badly written proof to a competitive math problem. I guess I could expand it slightly if readers find it unreadable. The following is a question from the International Mathematics Competition, 1994. Prove that in any set of different irrational numbers, there exist irrational numbers such that for any such that (1) andContinue reading
Fruits of procrastination 