Carmichael Number/Examples/1729

Example of Carmichael Number
$1729$ is a Carmichael number:
 * $\forall a \in \Z: a \perp 1729: a^{1729} \equiv a \pmod {1729}$

while $1729$ is composite.

Proof
We have that:
 * $1729 = 7 \times 13 \times 19$

and so:

We also have that:

The result follows by Korselt's Theorem.