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Theory of numbers.

Author: Bonnie Madison Stewart
Publisher: New York, Macmillan [1964]
Edition/Format:   Print book : English : 2d edView all editions and formats
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Additional Physical Format: Online version:
Stewart, Bonnie Madison.
Theory of numbers.
New York : Macmillan, 1964
(OCoLC)899750838
Document Type: Book
All Authors / Contributors: Bonnie Madison Stewart
OCLC Number: 525587
Description: xiv, 383 pages illustrations, diagrams 25 cm
Contents: pt. I. An intuitive approach. Preliminary considerations --
Mathematical induction --
The division algorithm --
Number theory in the game of solitaire --
Representation of the integers --
The Euclid algorithm --
More about greatest common divisors --
The fundamental theorem of arithmetic --
Prime and composite integers --
The number-theoretic functions [tau](n) and [sigma](n) --
Multiplicative number-theoretic functions --
The bracket function --
Introduction to the congruence notation --
Linear congruences --
Diophantine equations of the first degree --
Systems of linear congruences --
The Euler-Fermat theorems --
Congruences of higher degree --
Exponents and primitive roots --
The theory of indices --
Quadratic residues and Legendre's symbol --
The quadratic reciprocity law --
Pythagorean triplets --
Homogeneous quadratic Diophantine equations --
Fermat's method of descent --
Sum of four squares --
Sum of two squares --
Egyptian fractions --
pt. II. An axiomatic approach. Mathematical systems and introduction to group theory --
Transformation groups --
Linear transformations and matrices --
Introduction to quadratic forms --
Congruence modulo a subgroup --
Direct products --
Rings, domains, and fields --
The fundamental theorem reconsidered --
Quotient fields --
Ordered rings --
Polynomial rings --
Modular fields --
The real field and decimal representation of rational numbers --
Continued fractions --
Peano's axioms for the natural integers --
Integers-positive, negative, and zero.

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