The theorem below is from the book “Elementary Number Theory” by “David Burton”
“Let n be a composite square-free integer, say, n = p1 p2 · · · pr , where the pi are distinct primes. If pi−1|n−1 for all i=1,2,...,r, then n is an absolute pseudoprime.”
The proof in the book considers only the case where gcd(a, n) is equal to 1. Can somebody please complete the proof when gcd(a, n) ≠ 1 ?
