Carmichael Number/Examples/561

Example of Carmichael Number
$561$ is a Carmichael number:
 * $\forall a \in \Z: a \perp 561: a^{561} \equiv a \pmod {561}$

while $561$ is composite.

Proof
We have that:
 * $561 = 3 \times 11 \times 17$

and so:

We also have that:

The result follows by Korselt's Theorem.