# History of the Theory of Numbers

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*Leonard Eugene Dickson*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

Dickson's History is truly a monumental account of the development of one of the oldest and most important areas
of mathematics. It is remarkable today to think that such a complete
history could even be conceived. That Dickson was able to accomplish
such a feat is attested to by the fact that his History has
become the standard reference for number theory up to that
time. One need only look at later classics, such as Hardy and Wright,
where Dickson's History is frequently cited, to see its
importance.

The book is divided into three volumes by topic. In scope, the
coverage is encyclopedic, leaving very little out. It is interesting
to see the topics being resuscitated today that are treated in detail
in Dickson.

The first volume of Dickson's History covers the related
topics of divisibility and primality. It begins with a description of
the development of our understanding of perfect numbers. Other
standard topics, such as Fermat's theorems, primitive roots, counting
divisors, the Möbius function, and prime numbers themselves are
treated. Dickson, in this thoroughness, also includes less workhorse
subjects, such as methods of factoring, divisibility of factorials and
properties of the digits of numbers. Concepts, results and citations
are numerous.

The second volume is a comprehensive treatment of Diophantine
analysis. Besides the familiar cases of Diophantine equations, this
rubric also covers partitions, representations as a sum of two, three,
four or \(n\) squares, Waring's problem in general and
Hilbert's solution of it, and perfect squares in arithmetical and
geometrical progressions. Of course, many important Diophantine
equations, such as Pell's equation, and classes of equations, such as
quadratic, cubic and quartic equations, are treated in detail. As
usual with Dickson, the account is encyclopedic and the references are
numerous.

The last volume of Dickson's History is the most modern,
covering quadratic and higher forms. The treatment here is more
general than in Volume II, which, in a sense, is more concerned with
special cases. Indeed, this volume chiefly presents methods of
attacking whole classes of problems. Again, Dickson is exhaustive
with references and citations.