Annotated Web Links

CHAPTER 14 – The Gaussian Integers
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14.1    Gaussian Integers and Gaussian Primes

 

Page 549

 

Properties of the Gaussian integers are explained at http://www.cut-the-knot.org/arithmetic/int_domain4.shtml  (Strange Integers – Gaussian Integers)

 

Page 552

 

An applet that graphically displays Gaussian primes can be found at http://www.alpertron.com.ar/GAUSSPR.HTM (Gaussian primes)

 

Page 559

 

Tsuchimura’s excellent survey article and the latest results for Gaussian moats can be found at http://www.keisu.t.u-tokyo.ac.jp/Research/METR/2004/METR04-13.pdf

 

 

14.2    Greatest Common Divisors and Unique Factorization

 

Page 560

 

An applet for expressing a greatest common divisor of two Gaussian integers as a linear combination of these integers can be found at http://www.math.fau.edu/Richman/bezout-g.htm (Bézout's equation for Gaussian integers)

 

 

Page 563

 

An applet for factoring Gaussian integers, as well as carrying out many different calculations with Gaussian integers,  can be found at http://www.alpertron.com.ar/GAUSSIAN.HTM (Gaussian integer factorization applet)

 

 

14.3  Gaussian Integers and Sums of Squares

 

Page 575

 

Conjectures about Gaussian integers can be found at http://www.mathpuzzle.com/Gaussians.html (The Neglected Gaussian Integers)

 

 

Appendix A
Axioms for the Set of Integers

 
Page 577

You can learn more about the Peano axioms at http://www.torget.se/users/m/mauritz/math/num/peano.htm (Peano's Axioms)

 

Appendix B

Binomial Coefficients

Page 582

Biographical information about Blaise Pascal can be found at the MacTutor History of Mathematics Archive at
http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Pascal.html (Pascal)

 

Appendix C

Using Maple and Mathematica for Number Theory

Page 589

The Maple home page is a good place to starting learning more about Maple: http://www.maplesoft.com (Waterloo Maple: Home)

 

Page 590

Maple worksheets written by John Cosgrave for a course in number theory and cryptography at St. Patrick's College in Dublin, Ireland can be found at
http://www.spd.dcu.ie/johnbcos/Maple_3rd_year.htm

You can find a Maple worksheet on the Collatz problem at

http://www.mapleapps.com/categories/mathematics/numbertheory/html/collatz.html

 

 

Page 593

Information on Mathematica can be found at http://www.mathematica.com
Mathematica packages can be accessed at http://www.mathsource.com

 

Page 594

A program for implementing the iterations in the Collatz 3x+1 problem in Mathematica can be found at http://library.wolfram.com/infocenter/Demos/153/

 

Page 595
You can find an implementation of the RSA Public-Key Cryptosystem in Mathematica at

http://library.wolfram.com/infocenter/MathSource/1966/

 

 

Appendix D
Number Theory Web Links

The links listed in this appendix are:

http://www.scs.surray.ac.uk/Personal/R.Knott/Fibonacci/fib.html (The Fibonacci Numbers and the Golden Section)

http://www.utm.edu/research/primes/ (The Prime Pages)

http://www.mersenne.org (The Great Internet Prime Search)

http://www-groups.dcs.st-and.ac.uk/history/index.html (The MacTutor History of Mathematics Archives)

 

http://www.cs.unb.ca/~alopez-o/math-faq/math-faq.html (Frequently Asked Questions in Mathematics)

http://www.numbertheory.org/ntw/ (The Number Theory Web)
 
http://www.rsa.com/rsalabs/faq/ (RSA Labs - Cryptography FAQ)

http://www.best.com/~cgd/home/flt/flt01.htm (The Mathematics of Fermat's Last Theorem)

http://www.pbs.org/wgbh/nova/proof (NOVA Online - The Proof)

 

Appendix E

TABLES

Page 601
You can find a table of the first 100,008 primes on the Prime Pages at http://www.utm.edu/research/primes/lists/small/100000.txt