Hidden in Plain Sight

Randolph Nelson
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Chapter Chapter 9 in A Brief Journey in Discrete Mathematics, 2020, pp 119-132 from Springer

Abstract: 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.

Date: 2020
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DOI: 10.1007/978-3-030-37861-5_9

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