# The Ultimate Challenge: The 3x+1 Problem

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The $3x 1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then ""multiply by three and add one"", while if it is even then ""divide by two"". The $3x 1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 \cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.

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## 1.Ultimate Challenge, The: The 3x + 1 Problem

ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218494080000000

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## 2.The Ultimate Challenge: The 3X+1 Problem (Hardback)

Editore: American Mathematical Society, United States (2011)
ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society, United States, 2011. Hardback. Condizione libro: New. 254 x 190 mm. Language: English . Brand New Book. The $3x 1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then multiply by three and add one , while if it is even then divide by two . The $3x 1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000. Codice libro della libreria AAN9780821849408

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## 3.The Ultimate Challenge: The 3X+1 Problem (Hardback)

Editore: American Mathematical Society, United States (2011)
ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society, United States, 2011. Hardback. Condizione libro: New. 254 x 190 mm. Language: English . Brand New Book. The $3x 1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then multiply by three and add one , while if it is even then divide by two . The $3x 1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000. Codice libro della libreria AAN9780821849408

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## 4.The Ultimate Challenge

Editore: American Mathematical Society (2011)
ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society, 2011. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821849408

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## 5.The Ultimate Challenge: The 3X"plus"1 Problem

Editore: American Mathematical Society
ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society. Hardback. Condizione libro: new. BRAND NEW, The Ultimate Challenge: The 3X"plus"1 Problem, Jeffrey C. Lagarias, The $3x 1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then ""multiply by three and add one"", while if it is even then ""divide by two"". The $3x 1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 \cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000. Codice libro della libreria B9780821849408

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## 6.The Ultimate Challenge: The $3x+1$ Problem

Editore: Amer Mathematical Society (2011)
ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro Amer Mathematical Society, 2011. Hardcover. Condizione libro: Brand New. reprint edition. 348 pages. 10.00x7.50x0.90 inches. In Stock. Codice libro della libreria __0821849409

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## 7.The Ultimate Challenge: The 3x+1 Problem

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ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society, 2011. Hardcover. Condizione libro: New. Reprint. Codice libro della libreria DADAX0821849409

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## 8.The Ultimate Challenge: The 3x+1 Problem

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ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society, 2011. Hardcover. Condizione libro: New. Codice libro della libreria P110821849409

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## 9.Ultimate Challenge (Hardcover)

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Descrizione libro 2011. Hardcover. Condizione libro: New. 261mm x 182mm x. Hardcover. The $3x 1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then multiply by three and.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 344 pages. 0.776. Codice libro della libreria 9780821849408

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## 10.The Ultimate Challenge

Editore: American Mathematical Society (2011)
ISBN 10: 0821849409 ISBN 13: 9780821849408
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Descrizione libro American Mathematical Society, 2011. Hardcover. Condizione libro: New. 15.2 x 22.9 cm. Our orders are sent from our warehouse locally or directly from our international distributors to allow us to offer you the best possible price and delivery time. Book. Codice libro della libreria MM-60848774

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