Lure of the integers

In some small way, this book is an introduction to a mythical book which might go under the name of The Book of Inegers. This mythical book has on page n all of the interesting properties of the integern. This introduction stems from the collection of many years casual accumulation of numerical facts. Most of the material presented belongs to elementary mathematics in the sense that no deep or profound mathematical background is required in order to understand what is said. Much of the material is drawn from the theory of numbers.

Many of the topics touch on contemporary research and most of the results are stated without proof. As a general rule, one cannot tell from the statements of the results whether or not their proofs will be elementary. Indeed, this is a hallmark of mathematics and is one of the things that gives the subject a special flavor and interest. Until one knows that expert practitioners have been unable to slove a problem, one does not know that the problem is difficult. Even then it may turn out that there is an easy solution.

Some of the material will be familiar to people having only a small acquaintance with mathematics. Even in these cases, the author tries to provide something new. On the other hand, much of the material is sufficiently out of the mainstream of concern that even professional mathematicians ma be unfamiliar with the results. The many references to the literature will almost always enable a reader to track down further information. In Lure of the Integers the author has presented a body of material that will prove interesting to the enlightened layman as well as to the professional.