In the definition of Carmichael number, why is it necessary to have $(b, n) = 1$?

In number theory, a Carmichael number is a composite number $n$ which satisfies the modular arithmetic congruence relation $$b^{n-1}\equiv 1\pmod{n}$$

for all integers $1

In the definition of Carmichael number, why is it necessary to have $(b,n) = 1$?

I need to understand this point, please.