Combinatorics and Graph Theory

Collatz Conjecture Confirmed Through Connectivity of Odd and 8mod12 Positive Integers

Authors: Chloe Patricia Williams
Comments: 10 Pages.

In this paper, I will prove all orbits beginning with an odd positive integer link incrementally through connected orbits to a power of two orbit. Orbits connecting to a power of two orbit must decrease to one because connected orbits share values and finish the same way. These orbits connect because of a function I defined based on the connection between all odd and 8mod12 positive integers. Applying this function infinitely many times to all odd positive integers always leads to a connection to power of two orbits. With these results, I’m able to prove the conjecture.
Category: Combinatorics and Graph Theory