Carmichael Number/Examples/41,041

Example of Carmichael Number
$41 \, 041$ is a Carmichael number:
 * $\forall a \in \Z: a \perp 41 \, 041: a^{41 \, 041} \equiv a \pmod {41 \, 041}$

while $41 \, 041$ is composite.

Proof
We have that:
 * $41,041 = 7 \times 11 \times 13 \times 41$

and so:

We also have that:

The result follows by Korselt's Theorem.