Abstract
The integers larger than 1 are of two types: the composite integers which can be written as a product of two integers larger than 1 and the prime integers (or primes) which cannot. This book revolves around two questions: Given a composite integer, how do we find a decomposition into a product of integers larger than 1? How do we recognize a prime integer? Our investigation of these questions begins approximately 300 B.C. in the Greek city of Alexandria in what is today Egypt. There Euclid wrote his great work “Elements”, best known for its treatment of geometry but also containing three books on the properties of the integers.
“Euclid alone has looked on Beauty bare.”
Edna St. Vincent Millay (The Harp-Weaver)
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References
T. L. Heath, The Thirteen Books of Euclid′s Elements, Dover Publ. Co., New York, 1956.
Donald E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, 2nd ed., Addison-Wesley, Reading, MA, 1981.
Josef Stein, Computational Problems Associated with Racah Algebra, J. Computational Phys., 1(1967), 397–405.
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© 1989 Springer-Verlag New York, Inc.
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Bressoud, D.M. (1989). Unique Factorization and the Euclidean Algorithm. In: Factorization and Primality Testing. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4544-5_1
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DOI: https://doi.org/10.1007/978-1-4612-4544-5_1
Publisher Name: Springer, New York, NY
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