Abstract
In this chapter we introduce the concepts of order and the primitive root, two of the more fascinating and useful ideas in number theory. On the fundamental side, they helped the young Gauss to reduce the equation x16 + x15 + ... + x + 1 = 0 to several quadratic equations leading to the construction of the regular 17-gon. These same concepts also allow us to see why the decimal fraction of 1/7 has a period of length 6, while the decimal fraction for 1/11 has a period of only 2. And why does 1/99007599, written as a binary fraction, have a period of nearly 50 million 0’s and l’s? We shall see!
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References
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© 1986 Springer-Verlag Berlin Heidelberg
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Schroeder, M.R. (1986). Primitive Roots. In: Number Theory in Science and Communication. Springer Series in Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22246-1_13
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DOI: https://doi.org/10.1007/978-3-662-22246-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15800-4
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