Consider the following scenario:
Suppose A and B have set up their RSA public keys, namely $(e_a, n)$ and $(e_b, n)$, where the n-value is the same. Also, it happens that the $\gcd (e_a, e_b) = 1$. Suppose C wants to send both A and B a message $M$ that is coprime with $n$. Thus, C encrypts $M$ using A and B's public keys, producing the cipher text, $C_a$ and $C_b$.
I was told by my instructor, that suppose if there is someone who obtains the values of both $C_a$ and $C_b$, that particular person can determine the message $M$ using the public keys of $A$ and $B$, without knowing their private keys. Why is it necessarily true? Any help would be highly appreciated!