Can a sequence of cotangent spheres be packed inside a sphere so that the reciprocals of all of the radii are integers, like the integral apollonian circle packings on http://en.wikipedia.org/wiki/Apollonian_packing?
2026-03-27 20:19:38.1774642778
integral apollonian sphere packing
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Yes - see the "bowl of integers". And if you want to go to higher dimensions, there's a paper of Graham et al.