Identification Numbers and Modular Arithmetic

  • David R. Finston
  • Patrick J. Morandi
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


The first topic we will investigate is the mathematics of identification numbers. Many familiar things are described by a code of digits; zip codes, items in a grocery store, and books, to name three. One feature to all of these codes is the inclusion of an extra numerical digit, called a check digit, designed to detect errors in reading the code. When a machine (or a human) reads information, there is always the possibility of the information being read incorrectly. For example, moisture or dirt on the scanner used by a grocery store clerk can prevent an item’s code from being read correctly. It would be unacceptable if, because of a scanning error, customers were charged for caviar when they are buying tuna fish. The use of the check digit allows for the detection of some scanning errors. If an error is detected, the item is re-scanned until the correct code is read.

Supplementary material (31 kb)
Section-1.2-Exercise-8 (MW 31 KB) (29 kb)
Section-1.2-Exercise-14 (MW 30 KB)


  1. 1.
    Dudley U (2008) Elementary number theory, 2nd edn. Dover Books, New YorkzbMATHGoogle Scholar
  2. 2.
    Johnson B, Richman F (1997) Numbers and symmetry: an introduction to algebra. CRC, Boca RatonGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • David R. Finston
    • 1
    • 2
  • Patrick J. Morandi
    • 3
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.CUNY Graduate CenterNew YorkUSA
  3. 3.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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