The Fundamental Theorem of Arithmetic

J. J. P. Veerman ()
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J. J. P. Veerman: Portland State University

Chapter Chapter 2 in Numbers from all Angles, 2026, pp 19-37 from Springer

Abstract: Abstract We derive the fundamental theorem of arithmetic. The most important part of that theorem says every positive integer is essentially a unique product of primes. While this is a basic fact taught in elementary school, its proof is subtle and fundamental. We also discuss a few of its most important consequences, among others the fact that the number of primes is infinite. On the way to proving the fundamental theorem of arithmetic, we need some key results, namely Bézout’s lemma and Euclid’s lemma.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-10000-9_2

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DOI: 10.1007/978-3-032-10000-9_2

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