Maybe someone else has already pointed this out (or maybe everyone thinks it’s too obvious to bear pointing out), but the original question involved numbers that are either a square *or* thrice a square, not numbers that are a square *plus* thrice a square. (I’ve frequently encountered the set of numbers that are either square or pronic {1,2,4,6,9,12,16,20,...}, but that’s neither here nor there.) Jim Propp On Thursday, August 30, 2018, Dan Asimov <dasimov@earthlink.net> wrote:
Thanks for the explanations — how cool!
—Dan
----- From memory, as the drawing is still in some box (I moved):
I find squares on the x-axis and the 6 equivalent axes
(repeatedly multiply by w_6).
I find 3 * squares on the axis along w_{12} and the 6 equivalent axes (repeatedly multiply by w_6).
Best regards, jj
* Adam P. Goucher <apgoucher@gmx.com> [Aug 30. 2018 17:14]:
I'm using it to mean "arg(z) is a rational multiple of 2 pi", or equivalently "some power of z is real" or "z / abs(z) is a root of unity".
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