I'm reading about RSA and I have doubts:
1) To choose $e$, this value have to be between $1$ and $\phi=(p-1)(q-1)$, with $\gcd(\phi, e) = 1$, right?
2) In my example, $p = 139$ and $q = 491$. So $n = 68249$ and $\phi = 67620$. Assuming my point 1 is correct, $e$ can be $67619$. But $d$ can be $67619$ too, because $67619^2 \equiv 1 \mod 67620$.
Is this reasoning incorrect?