Category: Proofs

1988 IMO Problem 6
I found about this legendary problem from a Numberphile video and was intrigued. Go watch the video, even if you have seen the problem before. It’s fun! Here’s the problem which is can be found on The Official IMO page. 1988 IMO #6. Let $a$ and $b$ be positive integers such that $ab + 1$…

Uniqueness of Factorization
A few days ago I came across a proof of the Fundamental Theorem of Arithmetic (aka Unique Factorization) in Courant and Robbin’s What is MathematicsĀ that I hadn’t seen it before. I liked it enough to learn it. Then another surprise – I saw it again yesterday in Primes and Programming by Peter Giblin, a book…

Teaching Proofs
Here’s a nice guide to what is a proof and how to write one: How to write proofs: a quick guide by Eugenia Cheng. This is brief, has a nice outline, and gives some good examples. I love the analogy made, that a good proof is like a good story: it has a beginning, middle…