Number Theory

The Collatz Function and Topological Implementation of Catalan's Conjecture

Authors: Liam Isaac

The Collatz function is one of the simplest difficult problems in modern mathematics. For any positive integer, multiply any odd integer by 3 and add 1, while any even integer is divided by 2. Take the result and re-insert it into the function. Every integer will eventually fall to 1, and begin a loop of the sequence 1-4-2-1. Will this function produce another loop at some point? Will the jumps (3n+1) overtake the drops (/2) and climb to infinity? Through a nested fractal implementation as well as the reduction principle set in Catalan's Conjecture, it is shown that both of these questions are topologically impossible within the system.

Comments: 8 Pages. Creative Commons Attribution 4.0 International (CC-BY 4.0) (Note by ai.viXra.org Admin: Please cite listed scientific references)

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[v1] 2026-04-26 18:09:16

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