Number Theory

    

Reformulation of Syracuse Function and Its Convergence

Authors: Rakesh Timsina

This paper presents a geometrical approach to tackle the infamous Collatz conjecture. In this approach, we represent odd natural numbers as points in 2-D space. We then define a iterative geometrical algorithm and prove that this algorithm is equivalent to the Collatz function (more precisely, Syracuse function). Using the monotone convergence theorem, we prove the sequence generated by this algorithm always converges to 1. Since, this is same as saying Collatz (Syracuse) sequence converges to 1, we prove that the Collatz conjecture is true.

Comments: 9 Pages.

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Submission history

[v1] 2023-07-24 05:28:17

Unique-IP document downloads: 337 times

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