Linear Congruences

  • Manfred R. Schroeder
Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


Suppose a certain airline is consistently 25 hours late in departure and arrival (this has happened, but no names will be mentioned) while another one, flying the same route, is only 2 to 3 hours late. If you were in a hurry, which airline would you fly — food, lack of leg room and all else being equal? Obviously, being 25 hours late is as good (or bad) as being only 1 hour late. In other words, in a daily recurring event an extra day, or even several, makes no difference. The mathematics that deals with this kind of situation is called modular arithmetic, because only remainders modulo a given integer matter.


Path Difference Residue Class Chinese Remainder Theorem Composite Number Modular Arithmetic 
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  1. 6.1
    G.H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers, 5th ed., Sect. 5.2 (Clarendon, Oxford 1984)Google Scholar
  2. 6.2
    P. J. Davis: The Lore of Large Numbers (Random House, New York 1961)Google Scholar
  3. 6.3
    L. E. Dickson: History of the Theory of Numbers, Vols. 1–3 (Chelsea, New York 1952)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Bell LaboratoriesAcoustics Speech and Mechanics ResearchMurray HillUSA

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