Unique factorization and the fundamental theorem of arithmetic |
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Authors: | David Sprows |
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Institution: | 1. Department of Mathematics and Statistics, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USAdavid.sprows@villanova.edu |
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Abstract: | The fundamental theorem of arithmetic is one of those topics in mathematics that somehow ‘falls through the cracks’ in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like ‘every natural number can be broken down into a product of primes’. The fact that this breakdown always results in the same primes is viewed as ‘obvious’. The purpose of this paper is to illustrate with a number of examples that the ‘Unique Factorization Property’ is a rare property and the fact that the natural numbers possess this property is ‘fundamental’ to our understanding of this number system. |
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Keywords: | Factorization prime abundant number |
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