Dynamics of the iterated map $n \to 3n+1$ if $n$ is odd and $n \to \frac n2 $ if $n$ is even. Generalizations to $n \to 3n-1 $ or $ n \to 5n+1$ or even to $n \to pn+q$ . Other names are "$3x+1$-problem","syracuse problem". If you have a question, please be specific to your detail. MSE is not ...

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78
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9answers
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What is the importance of the Collatz conjecture?

I have been fascinated by this problem since I first heard about it in high school. From the Wikipedia article http://en.wikipedia.org/wiki/Collatz_problem: Take any natural number $n$. If $n$ is ...
13
votes
3answers
1k views

The $5n+1$ Problem

The Collatz Conjecture is a famous conjecture in mathematics that has lasted for over 70 years. It goes as follows: Define $f(n)$ to be as a function on the natural numbers by: $f(n) = n/2$ if $n$ ...
1
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1answer
280 views

Converse of Collatz Conjecture

How to write a pseudocode program that halts only if the Collatz Conjecture is false. Thanks much in advance!!!
6
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1answer
388 views

Required reading on the Collatz Conjecture

I am currently writing a paper on 3x+1 and realized that despite having enough knowledge to work on a singular facet of the problem I lack a more broad understanding of the problem. I have seen the ...
4
votes
1answer
238 views

Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.

For what values of $m,n$ natural, do $2^n - 1$ is divisible by $2^{m+n} - 3^m$? Thank you very much.
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2answers
478 views

About Collatz 3n+3?

While trying to prove the Collatz conjecture I came across the following Lemma : Lemma $1$ : All variables are positive integers. Define $Collatz(n)$ as the result of the (repeated) collatz ...
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1answer
493 views

Have 3n + 1 Problem Proof --But can't do the Mathspeak [closed]

I've come here as a last resort. When I first saw the Collatz conjecture I worked out pretty quickly what the dynamic was that drove the Collatz sequences. That was in 2009. Since then I've been ...
22
votes
4answers
825 views

Why is $3$ the coefficient of $n$ in the Collatz conjecture?

What's the importance of multiplying a odd number by $3$ and adding $1$, instead of just adding $1$? After all, if you add $1$ to an odd number then it turns into an even number. Here is a example ...
1
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1answer
404 views

What is known about Collatz like 3n + k?

I wonder what is known about variations of Collatz where $3n+1$ is replaced by $3n + 2k + 1$ where k is a fixed positive integer. In the OP ' about Collatz $3n+3$ ' it was confirmed that $3n+3$ ...
5
votes
3answers
79 views

How can I prove that an iterated transformation describes all odd integers?

This is a question where I want to find "a best" way (or even different ways) to prove my assumption - just to widen my understanding of similar problems and how to approach them. It's a question of ...
2
votes
1answer
73 views

Diophantine equation $3^{m}x+3^{m}-3^{m-i} 2^{i} +3^{m-i} 2^{i+s} -2^{m+s}=x 2^{m+s}$

As part of my research and my calculations I got the following diophantine equation. I do not have much experience with the diophantine equation. Is there any known method to solve it? Any help is ...
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2answers
673 views

What to do with Collatz proof? [closed]

I have discovered a proof solving the Collatz problem, and I have no idea what to do with it. Given the nature of the topic, all the experts I've found that are capable of reviewing the paper ...