This chapter returns to the question of deciding whether a given odd number m is prime. The a-pseudoprime test of Chapter 10B will not work on Carmichael numbers. We first describe an idea of Alford that shows that there are many Carmichael numbers. Then we develop the strong a-pseudoprime test and prove that every composite number m fails the strong a-pseudoprime test for at least half of the numbers a < m. Thus there are no composite numbers that are “strong Carmichael numbers”.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Carmichael Numbers. In: Childs, L.N. (eds) A Concrete Introduction to Higher Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74725-5_20
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DOI: https://doi.org/10.1007/978-0-387-74725-5_20
Publisher Name: Springer, New York, NY
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