I have a cipher system with $n=p_1\cdot p_2\cdot p_3$ , where every $p_i$ is prime , and a message $M$ ciphered in the following way $$E(M)=(M^{K_1})\mod n$$ I need to find the minimal number of unhidden messages in this system , and I have no clue where to even go.
thank very much for the help in advance
[Editor's note: from the comments an unhidden message is one where $E(M)=M$]
Hint: the CRT implies that $E(M)=M$ iff $M^{K_1} \pmod{p_i} \equiv M$ for $i=1,2,3$. So think about the prime situation first.