I need a detailed solution for this "math for information security" question.

We stated that the number 1105 is a Carmichael number, but we never checked that a 1105 a

(mod 1105) for every value of a. Get the factors of 1105 and use Fermats little theorem to prove That a 1105 a (mod Pi) every value of a, where Pi is a prime factor for 1105. Then explain why these congruences imply that a 1105 a (mod 1105) for every value of a.