I'm rereading my notes and they mention that $K_{23}(\mathbb Z) = \mathbb Z/(65520)$ This looks like a good point to stop and ask **whether there is any explanation** for this $K$-group of integers (23 is just an arbitrary fixed number for this purpose). By "explanation" I mean a reasoning that would allow to find at least some properties of this group in advance of computing it or some intuition behind the result. Here's one thing I already know: * non-torsion part of $K(\mathbb Z)$ is $\mathbb Z$ in degrees $0,5,9,13,\dots\ $ so $K_{23}(\mathbb Z)$ is pure torsion [Wikipedia](http://en.wikipedia.org/wiki/Algebraic_K-theory#Algebraic_K-groups_of_rings_of_integers) says that "The torsion subgroups of $K_{2i+1}(\mathbb Z)$ ... have recently been determined."