Simple arithmetic statements equivalent to the proof of the Collatz conjecture (original) (raw)
Related papers
Collatz Conjecture - The Proof
Collatz Conjecture - The Proof, 2021
final version of this paper here -> https://www.researchgate.net/publication/351347153 In this paper, we prove the Collatz conjecture. We show that if a given number can be represented in a form of a certain specific equation then Collatz conjecture is true for that particular number. Next we propose a procedure that for a given number produces this specific equation and we prove that for every initial positive integer, such equation can be found.
The only five expressions of numbers which respect the Collatz conjecture
This is a mathematical letter that uses easy tools in order to prove some interesting results about the Collatz conjecture. This short article carries on the efforts of the previous article about the Collatz conjecture which proves easily an interesting useful sequence with some other results by following a logical method. This work demonstrates also an interesting result which is the five only expressions of the numbers which respect the Collatz conjecture. This result may simplify many other demonstrations regarding the Collatz conjecture. Hence, I invite the readers to discover this content in order to make a new step towards the proof of this beautiful useful conjecture.
The Collatz Conjecture A PROPOSAL FOR ITS SOLUTION
The Collatz Conjecture A PROPOSAL FOR ITS SOLUTION, 2024
The purpose of this paper is to give a proposal for solving the Collatz conjecture. If the conjecture is taken to refer to finite integer positive numbers however large and finite sets however large, without reference to infinity, then the conjecture is proved to be valid.
Collatz conjecture states that : start with any positive integer n. If the integer is odd, multiply it by 3 and add 1. If the number is even, keep on dividing it by 2 until an odd integer is obtained. After repeating this sequence again and again, one will be obtained as the final result. It is also known as the 3n+1 problem or the Ulam conjecture. This paper presents the proof of the collatz conjecture using the basic concepts of number theory.
Collatz conjecture revisited: an elementary generalization
Acta Universitatis Sapientiae, Mathematica, 2020
Collatz conjecture states that iterating the map that takes even natural number n to n 2 {n \over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.
The new sequence and the parity in Collatz conjecture
Not only mathematicians are interested by unsolved problems and conjectures but also a high number of students of all fields who are eager to explore the depth of mathematics. Also, many mathematics problems are related to some problems of logic which we encounter in our daily life and this makes even people who are not scientists very interested by the meanings of the unsolved conjectures and by the possibilities of the solution. This short article about the Collatz conjecture uses easy mathematical tools and represents a fruit of my interest regarding the problems and riddles which mathematicians find complicated. I hope that other researchers can use the results of this article as a collaboration to solve this famous problem. The students may also find in this work an easy introduction to the meanings of the Collatz conjecture.