So, re-read a few crumbs and had a breakthrough this eve!
Finally understood the problem: big square, little square, to the point I can picture the whole thing in mind clearly now.
That enabled an excel model to be put together to brute force it, which is working. Not efficient, but a step on a path.
It takes about 1 min to factor a 10-digit "c". Lots of extra functions and lookups being done that aren't needed for display purposes, and about 5000x more computationally intensive than needed (see comments below). Ironically, the our beloved 145 case takes about the same time, as it does what it does, isn't smart.
Attached are a couple examples (see pics):
c=2,171,394,821
e=71,980
a=42,043
b=51,647
Small square = 42,043
Large square = 4,802
and
c=9,806,432,891
e=111,893
a=91,583
b=107,077
Small square = 7,747
Large square = 99,330
Some of that time was to calculate "e" which wasn't even being used.
But, knowing the "e" column, thus providing the d-pattern(s), would drastically reduce the table created (this proto just did linear D, still works).
So look at pic in post >>4097 for n=1, in any column, the D value is already around 2250 by the 33rd row (element). That's a 70x reduction in the search space. And matching 2 columns as done in this proto, that means it's 70x squared, or a 5000x reduction. Get it out of excel, this thing should humm.
Hey VA - you could try this in excel, screencapped the formula for you.
Here's the algorithm if someone wants to code it, should be straightforward. One column in the table is D, next column is D^2, and next is C+D^2.
Basically, just using the INDEX_MATCH function. Return row in COL_A (the "D"), where D^2 (COL_C) = C+D^2 (COL_M). That is the Large Square, returned in COL_N (have extra columns hidden not needed for this from when exploring how e=0 grew). Then, COL_O is the D for that row. Once you have Large and Small square, just a matter of plus and minus to get "a" and "b" (and use the "" if Cols N and O are blank).
In the excel model, Columns R, S, T, U have the same info in first row, just using a MIN function to find them, as it's hard to scroll through 100,000 rows to find where the match occurred.
Big night with Q too - takedown in China (with juicy intel re: the window and techniques) and big pharma treadmill vs cures. YUUGE! Feels like a winning day all round!!!
Thanks for the motivation everyone!
Think we've got this now!!!
Also believe VQC let us go down the triangle and other paths, as even if we don't need that for step 1, we're going to need it soon enough, and we're learning math, and that's one of the goals.
BTW, everyone should read about the singer Chris Curtis as listed here: >>3862
That VQC is one clever Kiwi!!!
Not only a band called "The Searchers", read the whole archive, it's fun. Here's a snippet - note the tin-foil story, perfect for us conspeericy folks!
"Curtis's concept was a band with a core of three members: Curtis, Lord and Robbie Hewlett. The other musicians would be engaged whenever the core felt like it. "They would jump on and off the roundabout. But I left that party in a new band, Roundabout." said Lord.
Curtis would arrange for Daimler limousines to taxi him about and was charging the cost to Tony Edwards. Edwards realised that he had made a mistake agreeing to manage Curtis but he liked what he saw of Jon Lord. And Lord was also having problems with Curtis, who had started to use LSD. Lord returned from a few days away with The Flowerpot Men to find the entire flat covered in aluminium foil. Everything; even the furniture and the light bulbs.
Curtis moved out soon after this but he did tell Lord that he had a guitarist in mind for Roundabout. Curtis arranged for Ritchie Blackmore and his girlfriend to fly over from Hamburg, Germany and meet Tony Edwards. The meeting was a success for Blackmore, Edwards and Lord but they had no room for the erratic Curtis. They changed their name to Deep Purple and their first single was Joe South's "Hush", which Curtis had been playing in Lord's flat for months."
HERE HERE HERE!!!