Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Where is the flaw in this proof of the Collatz Conjecture?
Replies: 8   Last Post: Aug 1, 2013 11:58 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
b92057@yahoo.com

Posts: 1,183
Registered: 4/18/05
Re: Where is the flaw in this proof of the Collatz Conjecture?
Posted: Aug 1, 2013 11:58 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Thursday, July 25, 2013 7:06:40 AM UTC-7, ra...@live.com wrote:
> The conjecture states that:
>
>
>
> Given a positive integer n,
>
>
>
> If n is even then divide by 2.
>
>
>
> If n is odd then multiply by 3 and add 1
>
>
>
> Conjecture: by repeating these operations you will eventually reach 1.
>
>
>
>
>
>
>
> Proof:
>
>
>
>
>
>
>
> Let n be the smallest positive integer that is a counterexample to the conjecture.
>
>
>
> If n is even then it can be divided by two to give a smaller number, leading to a contradiction.
>


If n is even, then it cannot be the smallest possible
counter-example.
>
> Assume n = 4k + 1.
>

By definition n (even) = 3k + 1


> Multiply it by 3, add 1, and divide by 2 twice.
>
>
>
> The result is 3k + 1, a number smaller than n, leading to a contradiction. Therefore n has the form
>
>
>
> n = 4k - 1.
>
>
>
> Multiply by 3, add 1, and divide by 2.
>
>
>
> The result is 6k - 1. If k is odd, then 6k - 1 is one more than a multiple of 4, which is impossible, therefore k is even, and n has the form
>
>
>
> n = 8k - 1
>
>
>
> Multiply by 3, add 1, and divide by 2.
>
>
>
> The result is 12k -1, with k necessarily even. In this manner it can be proved that n must have the form 16k - 1, 32k -1, 64k -1, and so on, requiring n to be infinitely large, which is impossible.





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.