Given a public key $(e,n)$, if we are free to choose the plaintext does that mean we are able to generate any possible ciphertext in $Z_n$ ?
Because if we were given $e$ we can say that the decryption key is $e^{-1} = k \mod n$ and then choose the ciphertext we wish to generate, say $c$, perform $c^k$ and that shows that any ciphertext is "reachable" via encryption given a specific key and some plaintext?
Is that correct?
Edit: The question is theoretical so we assume we know both the public and the private key.