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CHAPTER 5 - Applications of Congruences
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5.1 Divisibility Tests

Page 189

 

An article about divisibility tests at Ivan Peterson’s MathTrek can be found at http://www.maa.org/mathland/mathtrek_08_19_02.html (Testing for Divisibility)

You can find a clear explanation, written by Robert L. Ward, why different divisibility tests work for numbers in decimal notation at
http://forum.swarthmore.edu/k12/mathtips/ward.html (Math Forum: Explaining the Divisibility Rules)

Page 194

Information on repunits, including the repunits known to be prime, can be found at http://www.utm.edu/research/primes/glossary/Repunit.html (The Prime Glossary: repunit)

 

 

 

5.2 The Perpetual Calendar

Page 195

A perpetual calendar implemented by Michael Bertrand in Java can be found at
http://www.execpc.com/~mikeber/calendar.html (Java Perpetual Calendar)

 

 

5.3 Round-Robin Tournaments

Page 200

An interesting algorithm for scheduling double round-robin tournaments where each team plays each other twice so that each time plays at home, and so that a variety of constraints can be met, can be found at
http://www.comp.nus.edu.sg/~henz/projects/acc/index.html (Sport Tournament Scheduling)

 

 

5.4 Hashing Functions

Page 202

A definition of hashing functions can be found at
 http://searchdatabase.techtarget.com/sDefinition/0,,sid13_gci212230,00.html (hashing)

A discussion of hashing functions from a cryptographic standpoint is available as part of the RSA Laboratories cryptography FAQ at
http://www.rsasecurity.com/rsalabs/faq/2-1-6.html (What is a hash function?)

 

5.5 Check Digits

Page 207

A comprehensive discussion of various schemes used to construct check digits can be found at
http://www.augustana.ab.ca/~mohrj/algorithms/checkdigit.html (Check Digits)

Page 209 

More information about ISBNs can be found at http://www.adams1.com/pub/russadam/isbn.html

 

Tools for working with ISBNs can be found at http://isbntools.com/ (ISBN tools)

 

Information about the conversion of ISBNs to a newer system of EANs can be found at http://www.isbn.org/standards/home/isbn/transition.asp

 

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You can find applets for computing check digits for various types of UPCs at
 http://www.export911.com/e911/coding/digiCalc.htm and at http://www.ablt.com/check_digit_calculator.php