I would like to show the following: Let $p$ and $q$ be distinct odd primes and $n = pq$, then $\varphi(\lambda(n))$ is the number of pairs $(e,d)$ such that $(e,n)$ and $(d,n)$ are public/private keys of an RSA cryptosystem and that $2 \leq \varphi(\lambda(n)) < \lambda(n)/2$, where $\lambda$ is the Carmichael function and $\varphi$ is Euler's totient function.
I don't really know how to start... can someone help me with this, please?
Thanks!