History Of The Theory Of Numbers: Diophantine Analysis - Brossura

Dickson, Leonard Eugene

Brossura

ISBN 10: 0486442330 ISBN 13: 9780486442334

Casa editrice: Dover Pubns, 2005

Riassunto

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.

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Contenuti

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. Liouville’s 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. Waring’s Problem and Related Results XXVI. Fermat’s Last Theorem Indexes

Product Description

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.

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2005
• ISBN 10: 0486442330
• ISBN 13: 9780486442334
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 803
• Contatto del produttore: non disponibile