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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the number of false witnesses for a composite number


Authors: Paul Erdős and Carl Pomerance
Journal: Math. Comp. 46 (1986), 259-279
MSC: Primary 11Y11; Secondary 11N56
MathSciNet review: 815848
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Abstract: If a is not a multiple of n and $ {a^{n - 1}}\;\nequiv\;1\bmod\,n$, then n must be composite and a is called a "witness" for n. Let $ F(n)$ denote the number of "false witnesses" for n, that is, the number of $ a\bmod n$ with $ {a^{n - 1}} \equiv 1\bmod n$. Considered here is the normal and average size of $ F(n)$ for n composite. Also considered is the situation for the more stringent Euler and strong pseudoprime tests.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0815848-X
PII: S 0025-5718(1986)0815848-X
Article copyright: © Copyright 1986 American Mathematical Society