Looking into this post from last thread: >>9395

>If we were to look at an element that is d * d, a + b for that element would be (d + d), or 2d

We know from someone's Twitter dms with Chris quite a long time ago now that the fabled "root of d" that Chris has cryptically mentioned before is an element in (0,n).

>Root of d = {0, 2xd, 3xd, 2xd, d, 9xd}. All a and b of ( 0, 2xd, t) are multiple of d for all t.

>Yes and that pattern can be used elsewhere.

So if 2d is a representation of a+b for dd squares, and it has a directly calculable element related to it in (0,n), maybe there's something interesting to be found looking at (0,a+b).

What I've found looking into (0,a+b) is interesting I guess, but a lot of it is just basic arithmetic if you think about it. Using the same arithmetic from the root of d element, you'll find (most) (0,a+b) cells have an element at x=2(a+b). Some of them don't. These appear to be where n is twice a square (this sequence follows a different pattern which I'm pretty sure I went over in grid patterns). I remember there being another sequence of n values that didn't follow the same patterns in column 0 but I don't remember anything more specific since it's been a while since I did any actual work on this.

For the cells that do show up in (0,a+b) where x=2(a+b), the cell follows the same pattern as the root of d element except with i instead of d (since a+b=2i). Also, given i=d+n, the difference between each variable in both elements is the same multiplier by n. So, as follows:

<Root of d = {0, 2d, 3d, 2d, d, 9d}

<Root of i = {0, 2i, 3i, 2i, i, 9i}

<Difference = {0, 2n, 3n, 2n, n, 9n}

I didn’t really find anything all that interesting other than that (at least specifically about root of a+b). I'll make another post when I'm done putting code together in relation to the other posts about the link between the elements d is between in (e,1) and the cells in (0,n) that factorize dd.