Data Structures and Algorithms


Proof of Collatz' Conjecture

Authors: Robert Deloin

Collatz' conjecture (stated in 1937 by Collatz and also named Thwaites conjecture, or Syracuse, 3n+1 or oneness problem) can be described as follows: Take any positive whole number N. If N is even, divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat this process to the result over and over again. Collatz' conjecture is the supposition that for any positive integer N, the sequence will invariably reach the value 1. The main contribution of this paper is to present a new approach to Collatz' conjecture. The key idea of this new approach is to clearly differentiate the role of the division by two and the role of what we will name here the jump: a = 3n + 1. With this approach, the proof of the conjecture is given as well as generalizations for jumps of the form qn + r and for jumps being polynomials of degree m >1.

Comments: 16 Pages.

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Submission history

[v1] 2016-11-26 05:11:34

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