The Fundamental Theorem of Arithmetic

  • Tom M. Apostol
Part of the Undergraduate Texts in Mathematics book series (UTM)


This chapter introduces basic concepts of elementary number theory such as divisibility, greatest common divisor, and prime and composite numbers. The principal results are Theorem 1.2, which establishes the existence of the greatest common divisor of any two integers, and Theorem 1.10 (the fundamental theorem of arithmetic), which shows that every integer greater than 1 can be represented as a product of prime factors in only one way (apart from the order of the factors). Many of the proofs make use of the following property of integers.


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Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • Tom M. Apostol
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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