Combinatorics and Graph Theory

    

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

Authors: Chloe Patricia Williams

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.

Comments: 10 Pages.

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Submission history

[v1] 2025-07-03 17:36:12
[v2] 2025-11-22 00:23:52
[v3] 2026-03-13 19:39:34

Unique-IP document downloads: 596 times

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