Happy birthday. I'll get my big integer library ready.
While VQC is finishing his family lunch, I'm going to just do some prep to see if I'm on board.
LookupT(145) =67, 1, 24
So at (1, 1, 67) (e,n,t) we have 145 * 61, and this record also exists in e=1, f=-24.
We know the record a=5, b=29 exists in (1, 5) and in (-24, 4).
The square of 145 exists in (0, 1, 145), (0, 1, 145*2) ..
The question then is
>X and Y are the positions of n between 1 and the square of c
Are we referring to the two n-values as in n=5 and n=4, or the bigN and the mirror bigN?
We know c^2 exists in both (0, 1) and (1, 1). In the first column it's the a-value and exists at x=2c, while in the second it's a d-value and exists at x=(2c-1).
Also:
> LookupT is used by LookupN.
A reference to the recursiveness of the algorithm? If so, we're then dealing with first starting from c, finding some record based on this and then continue?
I'm seeing this as two possible things, either it is a reference to the pattern:
a[t] = bn
d[t - 1] - d = b(n-1)
or, it's more literal as in there are two values in (e, 1) where (d[t] + x)/2 = d. As in, d is between these two numbers.
For the first part I haven't had luck in the past trying to figure out how to take advantage of it, since (-f, -1) the a-values are all equal to the d[t] - d from (e, 1). The d[t - 1] is a point, however, to how the patterns move. Since -f is looking at c from another perspective (d + 1) you can look at c from multiple such perspectives (d + 1 … 10000) and you'll see how the t-patterns moves as a square throughout all the f-s (or rather a grid of squares).
For the second idea we have to involve the negative x-values, something you've been pushing on us a lot. So for our example of c=145, d = 12. If we're after the midpoint, that is where (d[t] + d[k])/2 = d we have d[2] = 8 and d[5] = 32.
(-8 + 32)/2 = 12 and (8 + (-32))/2 = 12.
In this case d[2] = 8, a[2] = 5 and d[5] = 32, a[5] = 25.
All right then. See you later tonight. Continue to have a happy birthday.