A cute combinatorial identity

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”


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