I put a continued fraction at
which came out very well, that is exactly how I like to display these. I will leave that section in place regardless.
However, I would like to place a second image of the same thing below, in some way smaller, so that the entire calculation fits within the intended answer box and does not overlap the text on the right hand side (currently Hot Network Questions). I can think of: successfully make a landscape style jpeg and upload that?; somehow make the same Latex display in smaller font size?? For something much longer or more like a sequence of related equations, I would just split into two lines, which is what I did on paper at home when doing the calculations.
So that's the question, what are some ways to do this?
In the answer by quid, the size command \tiny is probably too small, and MSE refused the command \footnotesize (I checked, I spelled it correctly). I was pleasantly surprised to find the command \scriptsize just right for the purpose. I repeated the final line in full size numbers but without big spacing, as a big part of the lesson is that, in Pell convergents for $\sqrt d,$ the value of $x^2 - d y^2$ also repeats.