What is the private key in RSA? I'm new to cryptography and I have a doubt: I read some pages a bit different definition for the RSA private key:

In 1 - (n, d)

In 2 - (d)

In 3 - (n, p, q)

Should I consider all these answers as correct? I know that if you have d and the public key, you have n (and e), and I know pq = n too.
For private key operations you need at least $n$ (the modulus) and $d$ (the private exponent). The primes $p$ and $q$ let you calculate those – or use some shortcuts for quicker computation – so they also suffice.

In practice RSA keys often include all of those values, to avoid having to compute them as needed and to allow for optimized and unoptimized implementations.


  In 2 - (d)


This would not be enough on its own, but the page actually says that the private key includes the modulus.