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A Brief Journey in Discrete MathematicsHidden in Plain Sight

A Brief Journey in Discrete Mathematics: Hidden in Plain Sight [Take any number and keep finding factors of that number that cannot be factored themselves. For example, 84 = 2 ⋅ 2 ⋅ 3 ⋅ 7, 455 = 5 ⋅ 7 ⋅ 13, or 897 = 3 ⋅ 13 ⋅ 23. These examples show that a number can be written as the product of prime numbers. This is called a prime factorization. A separate argument, that we will shortly get to, shows that this factorization is unique. This result has far reaching consequences and is called the Fundamental Theorem of Arithmetic. This theorem shows that primes are the DNA of the number system. Essentially all of the results of number theory are theorems of the primes, the topic of this chapter.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Brief Journey in Discrete MathematicsHidden in Plain Sight

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2020
ISBN
978-3-030-37860-8
Pages
119 –132
DOI
10.1007/978-3-030-37861-5_9
Publisher site
See Chapter on Publisher Site

Abstract

[Take any number and keep finding factors of that number that cannot be factored themselves. For example, 84 = 2 ⋅ 2 ⋅ 3 ⋅ 7, 455 = 5 ⋅ 7 ⋅ 13, or 897 = 3 ⋅ 13 ⋅ 23. These examples show that a number can be written as the product of prime numbers. This is called a prime factorization. A separate argument, that we will shortly get to, shows that this factorization is unique. This result has far reaching consequences and is called the Fundamental Theorem of Arithmetic. This theorem shows that primes are the DNA of the number system. Essentially all of the results of number theory are theorems of the primes, the topic of this chapter.]

Published: Feb 12, 2020

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