The set-up of the problem is simple. Define the function below on the natural numbers.
|The "phi" funcion|
The problem is to prove that if you start with any natural number and repeatedly apply this function, you will eventually get back to 1. For example:
- 4 -> 2 -> 1
- 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
Many people have tried to prove the Collatz Conjecture, and none have yet succeeded. For me, the draw is that I can feel that there is a solution on the tip of my tongue. It is the feeling that comes when you know there is a solution that you will see when you look at the problem in the correct way. Despite that feeling, I have yet to find the solution.