Mathematics

A Conjecture About The Collatz Conjecture

Is it possible the Collatz conjecture only needs to be solved for odd numbers?

Photo by Antoine Dautry on Unsplash

Don’t worry, I am not trying to prove the Collatz Conjecture (nope, nope, nope, — not going down that rabbit hole.) But I will be presenting an observation (my own conjecture.)

What is the Collatz Conjecture?

As a quick refresher, or introduction, let’s review what the Collatz Conjecture is.

The simple and, as yet unproven Collatz Conjecture, was put forth by Lothar Collatz in 1937.

The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1

As mentioned above, all we do is perform two simple arithmetic operations repeatedly, on any positive integer, and we always end up with the number 1.

By the way, there are many names for this conjecture. One of the most common is the 3n + 1 problem.

How It Works

We start with any positive integer, n > 0.

• Even Rule: If the number n is an even number, we divide…