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Carmichael's Conjecture

Carmichael's conjecture asserts that there are an Infinite number of Carmichael Numbers. This was proven by Alford et al. (1994).

See also Carmichael Number, Carmichael's Totient Function Conjecture


Alford, W. R.; Granville, A.; and Pomerance, C. ``There Are Infinitely Many Carmichael Numbers.'' Ann. Math. 139, 703-722, 1994.

Cipra, B. What's Happening in the Mathematical Sciences, Vol. 1. Providence, RI: Amer. Math. Soc., 1993.

Guy, R. K. ``Carmichael's Conjecture.'' §B39 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 94, 1994.

Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. ``The Pseudoprimes to $25\cdot 10^9$.'' Math. Comput. 35, 1003-1026, 1980.

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, pp. 29-31, 1989.

Schlafly, A. and Wagon, S. ``Carmichael's Conjecture on the Euler Function is Valid Below $10^{10,000,000}$.'' Math. Comput. 63, 415-419, 1994.

© 1996-9 Eric W. Weisstein