I understand how RSA crytosystem works, however I am not sure how to apply it to answer these questions. Can someone explain please?
Let $N=3869$ and be the product of two distinct unknown odd prime numbers $p$ and $q$ such that $(p − 1)(q − 1)$ is not divisible by $3$. Show that there are exactly nine messages which are unchanged by RSA encryption using the public key $(N, 3)$.
Also explain how to find p and q if at least four of these messages are known.