You're onto it: what you say would still need to be proven is actually not even true, see anderskaseorg's comments, e.g. https://news.ycombinator.com/item?id=17

You're onto it: what you say would still need to be proven is actually not even true, see anderskaseorg's comments, e.g. https://news.ycombinator.com/item?id=17104624 https://news.ycombinator.com/item?id=17104624. So their picture is nice, and the gcd!=1 cells are all red, but the gcd=1 cells need not be black. For odd N this fails loads of times (always?), and for even N you quickly find failing cells when you start looking for it (see linked comment).