''History of the Theory of Numbers'' is a three-volume work by
Leonard Eugene Dickson
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also rem ...
summarizing work in
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of
quadratic reciprocity
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard st ...
and higher
reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written .
Volumes
* Volume 1 -
Divisibility
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a ''Multiple (mathematics), multiple'' of m. An integer n is divis ...
and
Primality - 486 pages
* Volume 2 -
Diophantine Analysis - 803 pages
* Volume 3 -
Quadratic and Higher Forms - 313 pages
References
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External links
History of the Theory of Numbers - Volume 1at the Internet Archive.
History of the Theory of Numbers - Volume 2at the Internet Archive.
History of the Theory of Numbers - Volume 3at the Internet Archive.
History of mathematics
Mathematics books
Number theory
Squares in number theory
{{Math-hist-stub