A Carmichael number check

Check primes. For $a$ coprime to $1105$:
- mod $5$: $a^4\equiv1$, $1104=276\cdot4$, so $a^{1104}\equiv1\pmod5$.
- mod $13$: $a^{12}\equiv1$, $1104=92\cdot12$, so $a^{1104}\equiv1\pmod{13}$.
- mod $17$: $a^{16}\equiv1$, $1104=69\cdot16$, so $a^{1104}\equiv1\pmod{17}$.

CRT. Since $5,13,17$ are coprime, $a^{1104}\equiv1\pmod{1105}$.

Conclusion. $1105$ is a Carmichael number (like $561$).