The ultimate challenge

Description:

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 this 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 the history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number 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. Finally, the book reprints six early papers on the problem and related questions. -- from Back Cover.

subjects: Harmonic analysis,  Sequences (Mathematics),  Computer science -- Theory of computing -- None of the above, but in this section,  Polynomials,  Number theory -- Sequences and sets -- Recurrences,  Number theory -- Sequences and sets -- Special sequences and polynomials,  Dynamical systems and ergodic theory -- Ergodic theory -- Relations with number theory and harmonic analysis,  Number theory,  Collatz-Problem,  Reihe,  Iteration,  Polynom,  Folge,  Markov-Kette