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

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 trj Posts: 95 From: Korea Registered: 2/23/12
Re: Where is the flaw in this proof of the Collatz Conjecture?
Posted: Jul 25, 2013 10:20 AM

> 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

Yes.

>
> Assume n = 4k + 1.
>
> Multiply it by 3, add 1, and divide by 2 twice.
>
> The result is 3k + 1, a number smaller than n,
>
> n = 4k - 1.

Agreed.

> 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,

Why?

> 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

How?

> that n must have the
> form 16k - 1, 32k -1, 64k -1, and so on, requiring n
> to be infinitely large, which is impossible.

Date Subject Author
7/25/13 raycb@live.com
7/25/13 raycb@live.com
7/25/13 trj
7/25/13 Bart Goddard
7/25/13 raycb@live.com
7/25/13 raycb@live.com
7/25/13 Thomas Nordhaus
7/25/13 Gottfried Helms
8/1/13 b92057@yahoo.com