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On Numbers Analogous to the Carmichael Numbers

Published online by Cambridge University Press:  20 November 2018

H. C. Williams
H. C. Williams*
Affiliation:
University of ManitobaWinnipegMan. R3T 2N2
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A base a pseudoprime is an integer n such that

1

A Carmichael number is a composite integer n such that (1) is true for all a such that (a, n ) = l. It was shown by Carmichael [1] that, if n is a Carmichael number, then n is the product of k(>2) distinct primes P1,P2,P3, … Pk, and Pi-1|n-1(i=1, 2, 3, …, k).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 133 - 143
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Carmichael, R. D.. A new number theory function, Bull. Amer. Math. Soc., 19 (1910), pp. 232-238.Google Scholar
2. Chernick, Jack, On Fermat's simple theorem, Bull. Amer. Math. Soc., 45 (1939), pp. 269-274.Google Scholar
3. Lehmer, D. H., Strong Carmichael numbers, J. Aust. Math. Soc, Ser. A, 21 (1976) pp. 508-510.Google Scholar
4. Rotkiewicz, A, On the pseudoprimes with respect to the Lucas sequences, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 21 (1973), pp. 793-797.Google Scholar