Category:Carmichael Numbers

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This category contains results about Carmichael Numbers.
Definitions specific to this category can be found in Definitions/Carmichael Numbers.


An integer $n > 0$ is a Carmichael number if and only if:

$(1): \quad n$ is composite
$(2): \quad \forall a \in \Z: a \perp n: a^n \equiv a \pmod n$, or, equivalently, that $a^{n - 1} \equiv 1 \pmod n$.

That is, a Carmichael number is a composite number $n$ which satisfies $a^n \equiv a \pmod n$ for all integers $a$ which are coprime to it.