Synopses & Reviews
The three-volume series
History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.
Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.
Synopsis
This three-volume set, appropriate for upper-level undergraduate and graduate students, reviews the entire literature of number theory. Volume I focuses on material relating to divisibility and primality; Volume II, on the main landmarks of Diophantine analysis; and Volume III, on general theories rather than special problems and theorems. Accessible and well-indexed, the three books comprise the work of leading experts and can be used independently of each other.
Synopsis
This 2nd volume in the series
History of the Theory of Numbers presents material related to Diophantine Analysis. This series is the work of a distinguished mathematician who taught at the University of Chicago for 4 decades and is celebrated for his many contributions to number theory and group theory. 1919 edition.
Table of Contents
I. Polygonal, Pyramidal, and Figurate Numbers
II. Linear Diophantine Equations and Congruences
III. Partitions
IV. Rational Right Triangles
V. Triangles, Quadrilaterals, and Tetrahedra
VI. Sum of Two Squares
VII. Sum of Three Squares
VIII. Sum of Four Squares
IX. Sum of n Squares
X. Number of Solutions of Quadratic Congruences in n Unknowns
XI. Liouvilles Series of Eighteen Articles
XII. Pell Equation
XIII. Further Single Equations of the Second Degree
XIV. Squares in Arithmetical or Geometrical Progression
XV. Two or More Linear Functions Made Squares
XVI. Two Quadratic Functions of One or Two Unknowns Made Squares
XVII. Systems of Two Equations of Degree Two
XVIII. Three or More Quadratic Functions of One or Two Unknowns Made Squares
XIX. Systems of Three or More Equations of Degree Two in Three or More Unknowns
XX. Quadratic Form Made an nth Power
XI. Equations of Degree Three
XXII. Equations of Degree Four
XXIII. Equations of Degree n
XXIV. Sets of Integers with Equal Sums of Like Powers
XXV. Warings Problem and Related Results
XXVI. Fermats Last Theorem
Indexes