General rule of PRP

For any positive integer k, if it can be factored to the form
k=p1^m1*p2^m2*…*pn^mn
suppose q is a prime number such that q is not a factor of k,
then
Mod[q^(p*(p1-1)*(p2-1)*…*(pn-1)/（p1*p2*…*pn）), k]=1

Special: If k is a prime, and q is a different prime number,
Mod[q^(k-1), k] = 1