The Impossibility of Certain Types of Carmichael Numbers
نویسنده
چکیده
This paper proves that if a Carmichael number is composed of primes pi, then the LCM of the pi − 1’s can never be of the form 2 and can be of the form 2 ∗P for only four prime values of P ≤ 127. Moreover, if the LCM of a Carmichael number is 2 ∗ P and a Carmichael number m has all of its Fermat prime factors among the five known Fermat primes, then P must be one of the four possibilities mentioned above, and m can take one of only eight possible values.
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