In the RSA context, why is not safe to use the same n (public key)for different people?
The modulus is usually bound to the key pair. If somebody would want to sign or decrypt anything he/she would basically have to use the same private key. Obviously you cannot generate a valid private key if you only have knowledge about the public key, that would defeat RSA.
If you want a more theoretical answer, then I wish you luck and a good mathematical background.