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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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 Bart Goddard Posts: 1,706 Registered: 12/6/04
Re: Where is the flaw in this proof of the Collatz Conjecture?
Posted: Jul 25, 2013 10:32 AM

raycb@live.com wrote in

> 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

Why it is impossible? You've shown that the _smallest_ counterexample
can't be of the form 4k+1, but that doesn't apply to any other numbers.

You're confusing 'n' with its image under the operations.

> 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.

Same problem. n is 4k-1, not 8k-1 or 64k-1 or anything else.
You're confusing using k as a parameter and using it to describe
the form of the number.

B.

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