History of the Theory of Numbers, 3 volumes

''History of the Theory of Numbers'' is a three-volume work by

L. E. 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 reme ...

summarizing work in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

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 law In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f(x) with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irr ...

s 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 of m. An integer n is divisible or evenly divisible by ...

and

Primality A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

- 486 pages * Volume 2 -

Diophantine Analysis In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...

- 803 pages * Volume 3 - Quadratic and Higher Forms - 313 pages

References

* * * * * * * * * * * *

External links

History of the Theory of Numbers - Volume 1
at the Internet Archive.
History of the Theory of Numbers - Volume 2
at the Internet Archive.
History of the Theory of Numbers - Volume 3
at the Internet Archive. History of mathematics Mathematics books Number theory Squares in number theory {{maths-book-stub