Happy 2021!

Happy 2021 everyone! As a way to start out the new year, what’s better than an article about the mathematical properties of the number 2021 to prepare for the next Mathematical Team Competitions? To start out, 2021 is not a prime number, its factorization is: Hence, be prepared for a lot of chinese remainder theorem […]

A Problem From Stanford Mathematics Tournament 2008 (Team Test)

Daphne is in a maze of tunnels shown below. She enters at A, and at each intersection, chooses a direction randomly (including possibly turning around). Once Daphne reaches an exit, she will not return into the tunnels. What is the probability that she will exit at A? The Idea At first, I will denote by […]

IMO 2019/4

Find all couples of integers which satisfy The Idea We notice that work and we claim that other solutions don’t exist, so we want to get an upper and lower bound for . Proof Now let be the greatest exponent of prime in the scomposition of , we notice that and . Hence, Now we […]

Problem Solving Through Problems

One of the best mathematics book I’ve ever read is ‘Problem-Solving Through Problems’, by Loren C. Larson. The book is composed of 8 chapters. Each of these talks about a certain mathematical tool or topic. After a brief theory introduction, shows a lot of interesting example problems, which are very instructional and show how you […]

Problem Solving Strategies

A very interesting non-calculus mathematics book is ‘Problem-Solving Strategies’, by Arthur Engel. It gathers competition problems from over twenty national and international competitions of high school students.  The book is composed of 14 chapters. Each of these explains a particular mathematical concept, like the Extremal Principle, shows some exercises with solutions and then proposes some […]

Scroll to top