proposedproofs.blogspot.com

Proposed Proofs

Sunday, August 01, 2010. Collatz Conjecture: No Cycle: A One-Page Proof. Update Aug 2, 2010: Step #7 is wrong. I have found an error in my argument which invalidates the proof. This is meant to be a one-page proof based on my longer argument that I posted before. This one-pager attempts to show that there cannot be a cycle in a Collatz Sequence that does not include 1. Claim: A Collatz Sequence does not have cycles that do not include 1. 1 Assume that a Collatz sequence has a cycle of length n. A 2b 2c d.

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Sunday, August 01, 2010. Collatz Conjecture: No Cycle: A One-Page Proof. Update Aug 2, 2010: Step #7 is wrong. I have found an error in my argument which invalidates the proof. This is meant to be a one-page proof based on my longer argument that I posted before. This one-pager attempts to show that there cannot be a cycle in a Collatz Sequence that does not include 1. Claim: A Collatz Sequence does not have cycles that do not include 1. 1 Assume that a Collatz sequence has a cycle of length n. A 2b 2c d.

<META> KEYWORDS

1 proposed proofs

2 a each x

3 is odd

4 c each p

5 since x

6 is even

7 for the argument

8 let a

9 let b

10 let c

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proposed proofs,a each x,is odd,c each p,since x,is even,for the argument,let a,let b,let c,of p,let d,sum of p,for all p,each p,after x,let a =,sum p,because 1,then,0 comments,such that,where p,proof,so that,by collatz cycle,where,and n,which gives us

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Proposed Proofs | proposedproofs.blogspot.com Reviews

https://proposedproofs.blogspot.com

Sunday, August 01, 2010. Collatz Conjecture: No Cycle: A One-Page Proof. Update Aug 2, 2010: Step #7 is wrong. I have found an error in my argument which invalidates the proof. This is meant to be a one-page proof based on my longer argument that I posted before. This one-pager attempts to show that there cannot be a cycle in a Collatz Sequence that does not include 1. Claim: A Collatz Sequence does not have cycles that do not include 1. 1 Assume that a Collatz sequence has a cycle of length n. A 2b 2c d.

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proposedproofs.blogspot.com

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Proposed Proofs: Purpose

http://proposedproofs.blogspot.com/2006/09/purpose.html

Thursday, September 21, 2006. For the past year, I've been working on a blog that traces the history of number theory from the perspective of Fermat's Last Theorem. As an amateur, it has been fun and very rewarding to review the most important proofs in the history of number theory and present them in a roughly historical order. Please feel free to point out a flaw or to comment on how the proof can be improved. Posted by Larry Freeman at 10:05 PM. Fremont, California, United States.

2

Proposed Proofs: Collatz Conjecture: No Cycles

http://proposedproofs.blogspot.com/2010/07/collatz-conjecture-no-cycles.html

Saturday, July 31, 2010. Collatz Conjecture: No Cycles. Update (Aug 2, 2010): Lemma 12 is wrong. I do not believe that it can be corrected. This invalidates the argument. Definition 1: Collatz Sequence of Odd Integers. By collatz sequence of odd integers. I mean the integers x. And the integers p. Any odd integer greater than 1. Is the largest positive integer such that x. Is a positive odd integer. Lemma 1: In a Collatz Sequence of Odd Integers, any x. Where i 1 has the following relationship to x.

3

Proposed Proofs: July 2010

http://proposedproofs.blogspot.com/2010_07_01_archive.html

Saturday, July 31, 2010. Collatz Conjecture: No Cycles. Update (Aug 2, 2010): Lemma 12 is wrong. I do not believe that it can be corrected. This invalidates the argument. Definition 1: Collatz Sequence of Odd Integers. By collatz sequence of odd integers. I mean the integers x. And the integers p. Any odd integer greater than 1. Is the largest positive integer such that x. Is a positive odd integer. Lemma 1: In a Collatz Sequence of Odd Integers, any x. Where i 1 has the following relationship to x.

4

Proposed Proofs: Collatz Conjecture: No Cycle: A One-Page Proof

http://proposedproofs.blogspot.com/2010/08/collatz-conjecture-no-cycle-one-page.html

Sunday, August 01, 2010. Collatz Conjecture: No Cycle: A One-Page Proof. Update Aug 2, 2010: Step #7 is wrong. I have found an error in my argument which invalidates the proof. This is meant to be a one-page proof based on my longer argument that I posted before. This one-pager attempts to show that there cannot be a cycle in a Collatz Sequence that does not include 1. Claim: A Collatz Sequence does not have cycles that do not include 1. 1 Assume that a Collatz sequence has a cycle of length n. A 2b 2c d.

5

Proposed Proofs: September 2006

http://proposedproofs.blogspot.com/2006_09_01_archive.html

Thursday, September 21, 2006. For the past year, I've been working on a blog that traces the history of number theory from the perspective of Fermat's Last Theorem. As an amateur, it has been fun and very rewarding to review the most important proofs in the history of number theory and present them in a roughly historical order. Please feel free to point out a flaw or to comment on how the proof can be improved. Posted by Larry Freeman at 10:05 PM. Fremont, California, United States.

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Sunday, August 01, 2010. Collatz Conjecture: No Cycle: A One-Page Proof. Update Aug 2, 2010: Step #7 is wrong. I have found an error in my argument which invalidates the proof. This is meant to be a one-page proof based on my longer argument that I posted before. This one-pager attempts to show that there cannot be a cycle in a Collatz Sequence that does not include 1. Claim: A Collatz Sequence does not have cycles that do not include 1. 1 Assume that a Collatz sequence has a cycle of length n. A 2b 2c d.

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