Math wizards:
I believe there is only one solution to this for which r>k and that is 5/6. As to the how you get there, I have no idea.
$ \vert {\frac{427}{512} - \frac{k}{r}} \vert \leq \frac{1}{1024}$
(the two vertical lines represent the absolute value)
I can expand 427/512 but don't know how to get to k/r.
$\frac{427}{512} = 0+\frac{1}{1+\frac{1}{5+\frac{1}{42+\frac{1}{2}}}} $
Where I got this from there is a type of formula:
and then:
If anyone could explain how you get that formula, and how you go from the continued fraction expansion to $\frac{d_2}{r_2}= \frac{5}{6}$ tha'd be awesome!
:)