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An alternative and equivalent definition of Carmichael numbers is given by Korselt's theorem from [[1899]].
'''Theorem''' (Korselt 1899): A positive composite integer ''n'' is a Carmichael number if and only if ''n'' is [[square-free integer|square-free]], and for all prime divisors ''p'' of ''n'', it is true that ''p'' − 1 divides ''n'' − 1.
It follows from this theorem that all Carmichael numbers are [[odd number|odd]].
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