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Mar 2, 2017 at 16:38 vote accept Campello
Aug 21, 2014 at 8:39 history edited Aaron Meyerowitz CC BY-SA 3.0
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Aug 21, 2014 at 8:37 comment added Aaron Meyerowitz I updated to give better details. The claims I made before about when the ratio is outside $(0.99,1.01)$ involved calculations out far enough to be morally sure I had found all the records (and it turns out I was right.) But the results claimed now are guaranteed.
Aug 21, 2014 at 8:33 history edited Aaron Meyerowitz CC BY-SA 3.0
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Aug 20, 2014 at 10:55 comment added Campello I think it makes sense to allow all $r$'s such that $r^2$ is a sum of two squares (incidentally, in my computations I was assuming that $r$ is integer). Anyway, how did you prove that these are the record (and it never goes down again, for some "exciting" large $r$)?
Aug 20, 2014 at 2:06 history answered Aaron Meyerowitz CC BY-SA 3.0