This is a very gentle introduction to number theory, suitable for high school or beginning college students. The first edition was published in 1967. This 2017 second edition has been brought up-to-date with a light hand by John J. Watkins and Robin Wilson. They have brought the terminology up to date (we don’t say “aliquot parts” any more), made some rearrangements, updated the prime-number and other records, and added a few exercises. There is a new chapter on cryptography, and the reference list at the end has been updated with modern books (and a few classics),
This volume covers all the very most important number theory concepts, but just enough to given the reader a taste and a start. There are also a few topics that are not usually considered part of (academic) number theory, such as casting out nines, representations in other bases, magic squares, and cryptarithms. These do involve number-theoretic reasoning and will interest many students at this level.
In some ways this is a stripped-down version of Ore’s other book, Number Theory and its History. The prerequisites are not any higher for that volume, but it goes into much more detail and has many more worked examples.
I ran across Number Theory and its History in high school, and I adored it, mostly for its algorithms and numerical examples. The present book is relatively weak on those areas, and I probably would not have adored it, but it is full of interesting things and is worth showing to bright students.
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Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is allenstenger.com. His mathematical interests are number theory and classical analysis.