Henry Ibstedt - Surfing on the Ocean of Numbers

标签: 科学工程

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As the late, great Paul Erdos said, "If there is a problem that has remained unsolved for centuries, it is almost certainly one in number theory." Despite all the effort of so many talents, we may never know some of the basic properties such as if there are an infinite number of twin primes. Hence the charm of programming a computer search. In this book, Henry Ibstedt takes us on a journey where computers are used to explore the solutions to some simple problems in number theory. Very little is proven in the book, the emphasis is on the statement of a problem and the examination of the solutions for numbers in a selected range. Many of the problems are in the very hard to impossible category, although you never really know about problems in number theory.

Some examples of problems examined are:

Given (a,b) relatively prime, how many primes are there in the sequence ap(n) + b, where p(n) is the nth prime?
The Pseudo-Smarandache function Z(n) is the smallest integer m such that n divides 1 + 2 + 3 + . . . + m.
Iterations of d(n), the number of divisors function.
Iterations of sigma(n), the sum of divisors function.

The problems are all clearly stated and the charts and graphs easy to understand. Some of the results are what you would expect but others are not. In all cases, I found them worth examining.
If you love numbers and are looking for some problems that are a bit different from what you are accustomed to, then there is a high probability that you will like this book. (excerpted from Amazon.com reader's review)

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