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at http://mathworld.wolfram.com/CarmichaelNumber.html it says that a Carmichael number is one which satisfies Fermat's little theorem:

[tex]a^{n-1} \equiv 1 mod (n)[/tex]

foreverychoice ofawhich is co-prime ton, with 1 <a<n.

Why is the domain 1 <a<nspecified?

A maths book that I'm reading says "Can it happen that n is a pseudoprime to all possible bases a? The answer is yes and such numbers are called Carmichael numbers."

Does this mean that the set (1,n) exhausts all possible basesa?

Thanks :-)

Thomas.

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# On Carmichael Numbers

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