>Using an arbitrary divisor for f, then each of the eight triangles will have one OR one of two … configurations in each triangle.
Maybe that's the symmetry he's referring to.
>The symmetry is beautiful in the solution.
>When that symmetry cannot exist in more than one way, you have a neat way of spotting prime numbers.
If the arbitrary divisor for f gives one of two configurations, it exists in more than one way. I might be stating the obvious. I only came in here briefly and I'm not actually applying this to the math in my head. But we should be looking for a value of f that gives only one configuration in each triangle. So I think we'd find the answer if we took one triangle, found the correct value of f to give only one configuration in the triangles, and then compared it to other arbitrary values of f that give more than one configuration and looked for the differences between the singular f and the pluralur (I know that's not a word) f. That's if I'm reading into this right.