Congruences

  • Paul Erdős
  • János Surányi
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The exercises in Section 1.2 were concerned with divisibility properties. In many cases rules were studied for a given divisor that gave a new number significantly smaller than the dividend, both having the same remainder upon division by the divisor (e.g., for divisibility by 2, 3, 4, 5, 8, 9, 10, and 11). In general, this relation that two numbers have the same remainder upon division by a given divisor proves to be such a useful tool in number theory that Gauss introduced a special notation to represent it that quickly became part of almost every mathematician’s working vocabulary. Taking the names from Latin, we call two such numbers congruent, and their divisor the modulus.

References

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Paul Erdős
  • János Surányi
    • 1
  1. 1.Department of Algebra and Number TheoryEõtvõs Loránd UniversityBudapestHungary

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