Abstract
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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© 1976 Springer Science+Business Media New York
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Apostol, T.M. (1976). The Fundamental Theorem of Arithmetic. In: Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5579-4_2
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DOI: https://doi.org/10.1007/978-1-4757-5579-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2805-4
Online ISBN: 978-1-4757-5579-4
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