a2017c No.848 [View All]
Our task is simple. We are going to completely break the entire RSA cryptosystem!
And how are we going to do that?! With the VQC! Quick rundown to follow.
The main mathematical task that must be achieved to break RSA is to be able to factorize any integer instantly. The VQC is a promising way to do that.
What is the VQC?
The virtual quantum computer (VQC) is a grid made of infinite yet constructable sets that follow a known pattern. Like a quantum spreadsheet.
The grid is the superposition. The collapse of that superposition will be two input parameters, d and e which can be calculated easily for all integers, c, where c is the difference of two squares.
When the integers that are the difference of two squares are arranged into the grid and their corresponding properties are shown, a pattern emerges that shows calculation instead of searching is possible.
Legend
The map's legend is {e:n:d:x:a:b}, where d is the result of removing the largest square from c AKA the square root,
e is the remainder,
n is what you add to d to be exactly halfway between a and b,
and x is what you add to a to make d.
c is any number that is the difference of two squares, so odd numbers are included.
n*a and n*b for any c can be found n places apart in the cell at (e,1).
Rules of the grid: global rules
Each cell of the grid (e,n) has infinite elements or ZERO elements.
Each cell with one value has infinite elements, since every element can make a new one.
By induction, a cell only needs one value to make infinite values, that's part of the power of this and is why it is a virtual quantum computer as a whole.
The t variable is what will allow you to walk across these infinite elements.
If a grid cell has elements, all elements are constructable from a finite set of root elements.
The grid is indexed using e, n, and t, where e is the rows, n is the columns, and t is the specific element in the cell-group.
Thus, only three variables are required to identify an element: e, n and t.
All products of odd numbers and all products of pairs of even numbers are the difference of two squares.
The x-intercept of the line that goes through the point containing the factors of c is (a + 1).
(1, 1) - the key
The values of a and b at 1,1 are related to the length of the longest side in right angled triangles.
The values here can be used to create the entire grid.
The values here determine the values of the rows to the left and right, which determine the values of the whole column.
Columns
Each cell at n=1 contains the roots of products in the column.
If c is a prime number, it will appear in one column exactly once.
If c is the product of two prime numbers that do not equal eachother, c will appear in two cells of one column.
All products (integers) c that are the sum of two squares appear (only) in columns where e=0,1,4,9,16,25…
All factors in a column are factors of the elements of the first cell in their column.
All Fermat primes (except) 3 appear in column one.
(e, 1)
If a number at position t has a factor s, then s is a factor at (t+s), (t+2s) and so on for a at (e,1).
Also, if a number at position t has a factor s at (e+1), then s is a factor at (s+1-t), (2s+1-t), etc for a at (e,1).
Rows
(1, n)
The cells in row one where n=1 have a relationship with the cells 2n to the right and 2n to the left.
Each "a" from the first row equals na because xx+e = 2na and na is half of that. That's BIG part of the KEY
Each element in a cell can be generated by moving up (t-1 = x-2) or down (t+1 = x+2). Other variables can be generated from x.
Every single factor of any value of a in the first row will be referred to as s.
Want an even better quick rundown? Read VQC's introduction.
>>19
Useful Equations and Notation
ab = c
dd + e = c
(d + n)(d + n)-(x + n)(x + n) = c
a + 2x + 2n = b
a = d - x
d = a + x
d = floor_sqrt(c)
e = c - (dd)
b = c / a
n = the difference between the square root d and the larger of the two squares
n = ((a + b) / 2) - d
d + n = number that is exactly halfway between a and b
d + n = i
x = d - a
x = (floor_sqrt(( (d+n)*(d+n) - c))) - n
x + n = j
f = e - 2d + 1
t = the variable that lets you traverse the infinite elements in for a given (e, n) that has values.
if (e is even) t = (x + 2) / 2
if (e is odd) t = (x + 1) / 2
700 posts and 249 image replies omitted. Click [Open thread] to view. ____________________________
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15bf90 No.1685
>>1683
Agreed, Baker. No love for famefags. I'm just tripping out that Q is going mainstream. My lady is talking with friends on FB about who Q is, ie Barron, Don Jr, etc. WTF!!! When 60 million eyes get put on Q's posts, the world will redpill itself. AJ is talking openly about Q, chans, etc. Time to FIRE UP THE MEME CANNONS, LADS! I can't believe I'm alive to be seeing this. WHEN we solve this (with Senpai help, of course! Thx Senpai) we are going to help fundamentally change the course of human history. We have green light to go mainstream and fucking blast FB, Twatter, et al. I've been waiting for this moment my whole life, never thought it could really happen. Truth and Justice. Make Earth Great Again!
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e34200 No.1686
>>1684
Whoops I thought you were chirping us baker sorry I misinterpreted who you were calling famefags.
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15bf90 No.1687
>>1684
Yeah, thanks Baker! Can we get some more Victory ponies up in this??
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a2017c No.1688
>>1684
I'm not like you. I can't synthesize different areas of maths. I don't know what parabola's and roots are. I haven't had to brush up on them for this.
>>1685
Shame about Baruch. I guess they were right about him. I was in contact with him too.
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71e1c0 No.1689
>>1685
Indeed VA, just waiting for those Gitmo announcements! And for MSM to completely crumble.
Ok fags, here are some test cases and challenges for you:
RSA Test Cases and Challenges
https://pastebin.com/f5Km9K8H
RSA-100 (c) =
1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139
(100 decimal digits, 330 bits)
RSA-100 (a x b) =
37975227936943673922808872755445627854565536638199
×
40094690950920881030683735292761468389214899724061
(2 50 decimal primes)
RSA-100 (c^2) =
231832607105497859450453971149782249091397152352980773038383827802126335737279486733598563928061275517976566803851888280780332815207688528004235456616576727168746464977139224636030180916664018563207
(198 decimal digits)
–
RSA-129 (c) =
114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541
(129 decimal digits, 426 bits)
RSA-129 (a x b) =
3490529510847650949147849619903898133417764638493387843990820577
×
32769132993266709549961988190834461413177642967992942539798288533
(with a 64 and 65 decimal prime)
RSA-129 (c^2) =
13083156311017746081229837780584604971789185572322940113554957177463495238823718363789678158885976884237362181609103528581150260013472809482392451812847672930017596579807933662233072087386335238374806414971531141586419217198046250532235073881640972514818681
(257 decimal digits)
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71e1c0 No.1690
>>1689
RSA-190 (c) =
1907556405060696491061450432646028861081179759533184460647975622318915025587184175754054976155121593293492260464152630093238509246603207417124726121580858185985938946945490481721756401423481
(190 decimal digits & 629 bits)
RSA-190 (a x b) =
31711952576901527094851712897404759298051473160294503277847619278327936427981256542415724309619
×
60152600204445616415876416855266761832435433594718110725997638280836157040460481625355619404899
(with (2) 95 decimal primes)
RSA-190 (c^2) =
3638771438488087985574274106795079635808387100084863940611975142846520895542297425531641157043983476619993374723043826429566267790036775257657139728945914322148154407595065259459214885711856214268244428701532653022789206595392004837865259854410326840170456159370131034294156696408886672161241549375876666598321636136763746229426218477864974486848489396416573764495046083098157361
(379 decimal digits)
–
RSA-640 (c) = 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609
(193 decimal digits, 640 bits)
RSA-640 (a x b) =
1634733645809253848443133883865090859841783670033092312181110852389333100104508151212118167511579
×
1900871281664822113126851573935413975471896789968515493666638539088027103802104498957191261465571
(with (2) 97 decimal primes)
RSA-640 (c^2) =
9656048121330239196485739047236872733132646152415265572749839063571416858087801139297436736668535657942544532834166699749756556831546825766219543494478915395505001388433032706122580727561545005466558578465273868089134810944324056030967838960018632090507727101247760897728632535169583227345646104139213934877983671194311248207350399320919897813580637534250460303641423529457084273798881
(385 decimal digits)
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a2017c No.1691
>>1690
>>1689
Thanks for putting those together. Wikipedia has down syndrome so when I try to copy the RSA numbers it inserts a bunch of newlines.
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71e1c0 No.1692
>>1689
>>1690
And for some challenges, find a & b:
RSA-240 (c) =
124620366781718784065835044608106590434820374651678805754818788883289666801188210855036039570272508747509864768438458621054865537970253930571891217684318286362846948405301614416430468066875699415246993185704183030512549594371372159029236099
(240 decimal digits & 795 bits)
–
RSA-1024 (c) =
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256239341020864383202110372958725762358509643110564073501508187510676594629205563685529475213500852879416377328533906109750544334999811150056977236890927563
(309 decimal digits & 1,024 bits)
RSA-2048 =
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357
(617 decimal digits & 2,048 bits)
https://pastebin.com/f5Km9K8H
Godspeed PATHanons.
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15bf90 No.1693
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71e1c0 No.1694
>>1693
mr. spice and everything nice.
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427741 No.1695
>>1694
We gotta get to n from c. Wanna hop a Sandworm and cruise on over? ;)
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5f522a No.1696
Is anyone in touch with Inner/Outer Heaven?
I have a fresh angle to explore tomorrow, which has been looking me the face this entire time.
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427741 No.1697
>>1696
Do tell, MA. Inner/outer Heaven? What’s your intuition saying?
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5ba563 No.1698
>>1696
>Is anyone in touch with Inner/Outer Heaven?
>>1697
>Do tell, MA. Inner/outer Heaven? What’s your intuition saying?
It appears VA has outed himself as a newfag?
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3520dc No.1699
Ignore your squabbles.
You can watch the entirety of Star Trek: The Next Generation in the Q episodes alone.
VQC isn't "Albino Morpheus".
He's PICARD.
AS A Q!
I'm not even done with the episode, i've been through voyager… DS9 (999) is the ending.
Calling it now.
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3520dc No.1700
>>1699
dubs aside, i meant all of star trek after Qirq (Xerxes) landed us some attention.
I'll be back.
On a thing.
I'm….
Thing…
It's…
You know how I do.
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3520dc No.1701
>>1700
oh this is getting gooooooooood….
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3520dc No.1702
>>1701
pffffffffft
As if that wasn't already commented on where I'm seen elsewhere.
Love this.
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99edb0 No.1703
Oh fuck man I found a very important pattern. I need a minute.
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a2017c No.1704
>>1703
Share you faggot. We make progress by banging our heads on this wall together.
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99edb0 No.1705
>>1704
Do the words "I need a minute" mean nothing to you?
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3520dc No.1706
>>1704
FINE!
Linear progression applies, but if you have "the time"…
Tapestry:
Voyager
TNG
DS9
<;3=Q
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3520dc No.1707
>>1706
Janeway and Vash…
Personal Matter…
Also, halfway through memfarming I got cheeky so you fucking figure it out.
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3520dc No.1708
And for you fucking nerds who noticed.
https://youtu.be/byl0BLtO7UE
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99edb0 No.1709
Okay. As I mentioned here >>1647 (even though apparently I used the term genesis cell wrong; I was referring to the first cell of an infinite set), one way I was thinking we could find n from c was by finding i from c, since then we use n = i - d or n = i - (floor(sqrt(c))). Instead of spending half an hour turning this into something really easy to understand I'll just type out the process I took and hope everyone gets it and doesn't mind a whole bunch of text.
In order to figure out how to calculate i from c, since we can't do it with the variables we get from c alone, I tried to find a visual relationship between them. I made an image with a white pixel every time c is the product of two primes but instead of (e, n) as the axes it's (c, i). That's pic related. It shows the relationship between c and i, and it looks like a bunch of linear lines.
If these were linear, and we could figure out the relationship between these lines, we could use them to find i for a given c, couldn't we? All we'd need to do is find the correct line that our c is on and use simple gradient maths (rise / run). In order to confirm that these were linear lines, since it's a bit haphazard doing it in this Paint program I have, I changed the code around a little bit to plot each (c, i) as points in a big grid, much like the original {e, n, d, x, a, b} grid, but again with axes (c, i). I then highlighted from one point in each line to the next a few times in order to figure out the gradient. By the way, if anyone doesn't know, in whatever your spreadsheet software is, you can change the formula syntax to R1C1 and it'll change the x axis from letters to numbers, which is very handy (instead of something like BD24 it'll be something like R42C52, as in (42, 52)). In the next post I'll paste my calculations, since it'll break up the text a bit, and it'll show what the relationship is between these lines.
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99edb0 No.1710
>>1709
Lowest line
R121C52:R277C130
(121, 52) to (277, 130)
Rise is 156, run is 78, gradient is 2 (6/3)
R133C58:R265C124
(133, 58) to (265, 124)
Rise is 132, run is 66, gradient is 2 (6/3)
R337C160:R457C220
(337, 160) to (457, 220)
Rise is 120, run is 60, gradient is 2 (6/3)
Next line upwards
R169C116:R217C156
(169, 116) to (217, 156)
Rise is 48, run is 40, gradient is 1.2 (6/5)
R253C186:R289C216
(253, 186) to (289, 216)
Rise is 36, run is 30, gradient is 1.2 (6/5)
R289C216:R313C236
(289, 216) to (313, 236)
Rise is 24, run is 20, gradient is 1.2 (6/5)
Next line upwards
R217C204:R229C218
(217, 204) to (229, 218)
Rise is 12, run is 14, gradient is 6/7 (0.857142 repeat)
R229C218:R265C260
(229, 218) to (265, 260)
Rise is 36, run is 42, gradient is 6/7
R265C260:R301C302
(265, 260) to (301, 302)
Rise is 36, run is 42, gradient is 6/7
Next line upwards
R181C210:R205C254
(181, 210) to (205, 254)
Rise is 24, run is 44, gradient is 6/11 (0.545454545454)
Next line up
R181C222:R193C248
(181, 222) to (193, 248)
Rise is 12, run is 26, gradient is 6/13 (0.461538 repeat)
Next line up
R205C290:R217C324
(205, 290) to (217, 324)
Rise is 12, run is 34, gradient is 6/17
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a2017c No.1711
>>1601
Thanks, didn't notice until now. Will use those.
Oven is HOT.
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99edb0 No.1712
>>1709
>>1710
I did the next one too and it was 6/19. The thing you should all be taking away from this is that the denominators are all primes, and from the lowest line to the highest line they increase in order with 6 as the constant numerator.
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3520dc No.1716
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a2017c No.1717
>>1713
>>1713
>>1713
>>1713
>>1713
>>1713
Migrate when this thread is over. Good night.
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3520dc No.1718
oooh hoo hooo
This feels good, too
https://youtu.be/FJo6ipm7HqY
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99edb0 No.1720
>>1712
I didn't realize until now but setSize was 12. That means that while those gradient rules still work the numbers are slightly different. I'm currently trying to figure out the mathematical relationship between each line that determines where the next one starts each time.
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71e1c0 No.1723
>>1700
'What you realize becomes truth'
'Meme responsibly anons"
^^^THIS; works on several levels.
All-night digger. Layers deep, sauce within sauce. Perhaps more indictments / counts from this. Think the first class seat grabbing cunt was setup and blackmailed for control, affecting the homeland and our security. Tangled webs and boomerangs. More work to do, carry on anons.
>>1713 some tasty looking bread, tnx.
>>1531
Good oh Great Hobo. Define excession plz.
Unfamiliar w/ responsibilities associated with new threads, proposing a 'Disclosure, Ramifications, and Rebuilding' perhaps?
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01b9f7 No.1724
Tested!
For all records {0, n, c, c-aa, aa, bb}
A Goal record!
There is m such that n=2mm
and …
b-a = 2m
{0, 24200, 669, 660, 9, 49729)
m=110
b=223 a=3 a - b = 2m = 220
{0, 8, 77, 28, 49, 121}
m=2
b=11 a=7 a - b = 2m =4
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e34200 No.1725
Same as what I've been doing for constant D values (because for C record we already have correct D, so this could help us navigate through the D's:
pastebin. com/5cd4k2rz
Graph. (+ = from the end, *= extrapolated from pattern).
For any d, we can start off and say there will be an entry at
(e,n) = (-d^2,-d+1)
We can call this our origin cell for D. Now, to navigate along this graph we would need to generate cells from their (e,n,d) values, which I do not think we can do yet. However this pattern is still notable.
Starting at our origin cell (the Zeroth origin cell), (e,n) I THINK we can generate any cell for this pattern:
(e0,n0) -> (e0,n0+u) for any u [I'll go 70% on this step, cuz I can't generate to test, the other ones are pretty certain though]
Then, from our origin cell, if we go to the right one cell we get a second origin cell (origin cell 1). (e0,n0) -> (e0+1,n0) = (e1,n1) From this cell we can do
(e1,n1) -> (e1+2u, n1+u) to navigate down the line as many times as we want
Then, if we go down the line once (e1+n1)->(e1+2,n1+1) and then shift to the right (e1+2+1, n1+1) we get the third origin cell (e2,n2).
From the third origin cell, we can do:
(e2,n2) -> ( e2 + 4u, n2+u ) to generate more cells for any u.
Generally:
The zeroth origin cell for D can be found at:
(-d^2, 1-d).
For the zth origin cell, (e*,n*) we can generate any other entry with the same d by this equation:
(e*,n*) -> (e* + 2zu, n* + u)
Also, from any origin cell we can generate the next origin cell.
( z to z+1), which boils down to going down the line once and then adding 1 to e.
(e*,n*) -> (e* + 2z + 1, n* + 1)
So now we have a method to determine all the entries (e,n) with the same d. Also, this may be an impossible task, but if anyone can generate an entry just given the (e,n,d) values that would be sweet, but I don't think we can.
This may be the biggest thing I've discovered. This path for valid d values is the same for every d. As in, the only difference between entries for certain d values is the zero origin for d. Other than that you use the same exact steps to figure out what other cells have the same d. Knowing that, if we have a valid d, we can say, WITH SUPREME CONFIDENCE, that.
origin cell is at (-d^2, 1-d)
the origin cell for d-1 is at ( - (d-1)^2, 1-(d-1)) = (-dd +2d -1, -d) (same formula)
So if we have a cell we know for certain we can navigate to a valid cell by:
(e,n,d,x,a,b) -> (e+2d-1, n-1, d-1, x?, a?, b?)
to go down a d value.
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e34200 No.1726
>>1725
>>1725
The pattern for the origin cells is more consistent if the zero origin is calculated at (-d^2, -d) because that way you can still do the same pattern (go down the line once, then shift e by 1) to get the next origin cell. Before it was that pattern for all origins not equal to 0, now it is consistent.
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ac6203 No.1727
>>1725
>Also, this may be an impossible task, but if anyone can generate an entry just given the (e,n,d) values that would be sweet, but I don't think we can.
public static TheEndRecord CreateForEND( BigInteger e, BigInteger n, BigInteger d ) {
BigInteger c = d * d + e;
BigInteger x = ( Lib.Sqrt( ( d + n ) * ( d + n ) - c ) ) - n;
BigInteger a = d - x;
BigInteger b = a + 2 * x + 2 * n;
return new TheEndRecord( e, n, d, x, a, b );
}
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e34200 No.1728
>>1727
*holy fuck thanks for this code i would have been at a dead end without you*
a bit of output
>((-36, 0, 6, 6, 0, 12, 0), 'a=0')
>((-36, 1, 6, 6, 0, 14, 0), 'a=0')
>((-36, 2, 6, 6, 0, 16, 0), 'a=0')
>((-36, 3, 6, 6, 0, 18, 0), 'a=0')
>((-36, 4, 6, 6, 0, 20, 0), 'a=0')
>((-36, 5, 6, 6, 0, 22, 0), 'a=0')
Okay so I tested this code and and it only gave me values of A where A = 0. I used to have that a=0 meant an invalid cell, but heres the thing: For A=0, you can have ANY value for (e,n,d) that you want and they all could still be valid entries right? Like 0 is a number so why couldn't it be in entry a? Maybe these are all valid entries.
Suppose they are, our output from AB and C fun
C(21) = (5,7,4,3,1,21,21) = start
AB(3,7) = (5,1,4,1,3,7,21) = goal
So for this we have the correct E and D right off the bat. We may be able to iterate through these n values and search things from there, because these are valid cells, but we cannot do END(5,7,4) because I think it takes root of -1. But for this remember we have the correct D. So we can go to the (-d^2) column, which is basically the root for d ((-d^2,-d) would be the seed I guess). From that column, we can expand out and generate any cell for the same (correct) d. We could do this and iterate through the cells from each D origin cell and go down until we either hit or pass e. Then I think we may have our correct cell at that point.
Tada!
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ac6203 No.1729
>>1728
Iterating to find the solution isn't going to work.
See a couple of my previous posts:
>>1342
>>1487
>>1509
VA - thanks for reposting this. Am thinking this through a bit more.
We've been one variable or formula away from a solution for some time now.
The "Use Y on C at X" from >>>/cbts/75435 needs more attention.
I think we know what C and X are. And we know how to create a small square from t. What is Y? y axis? is that n?
CA got me thinking a bit more about the END formula.
c = (d+n)^2 - (x+n)^2
This can be solved a couple of ways. And given that we know c, d, and e for our target aa*bb and a*b records, perhaps if we can identify just the small square movement, we can solve for n.
For example:
Solving for x given n, d and c.
x = ( Lib.Sqrt( ( d + n ) * ( d + n ) - c ) ) - n;
Solving for n given e, d, and (x+n):
c = d*d + e;
n = Lib.Sqrt( c - (x+n)^2 ) - d
Maybe all we have to do is figure out the "small square" movement?
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13a210 No.1730
>>1729
When you're talking about the small square and the big square, do you mean X+N and D+N?
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ac6203 No.1731
>>1730
yes. I'm focusing specifically on the small square (x+n). It's relationship to t is simple. And it remains constant when you change e at (e,1,t).
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ac6203 No.1732
>>1731
forgot trip.
Also, if anyone can help explain "Use Y on C at X".
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a92e07 No.1733
Hey guys, its been a while between posts, but I've been following along with the progress.
I've been focused on my own theories mostly, and none have been fruitful.
>>1731
Hey PMA, the size of the small square has been where my attention has been lately.
I've also been spending some time going through reading for ECC.
I want to point out something that I've realized too…
n = (x^2 + e) / 2(d - x)
This is just a simple rewrite of x^2+e=2na.
But what I like about this representation, is that d and e are constants and so we have a relationship between n and x for any c.
I'm trying to use this equation to figure out the possible sizes of the small square.
Anyway, how is everyone?
Also welcome back CollegeAnon! How were your exams?
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ca62e5 No.1734
>>1731
>>1732
I like the idea. How do we deal with erratic t vars as n increases? Maybe we need a rewrite of t equations for larger n, or maybe the t vars are accurate in later n are accurate because the d,a,x vars create t? Basically, does t represent small square values as n increases and t begins to jump upward in patters rather than linear growth?
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ac6203 No.1735
>>1733
>I've also been spending some time going through reading for ECC.
I tried to read some of those documents… realized I'm not that smart.
>n = (x^2 + e) / 2(d - x)
I like the concept. After all, this seems to be an exercise in taking a really small square to it's perfect middle size.
>>1734
I believe this get's solved in the (e,1) space where there aren't any gaps in t. Remember, looking for one more variable or formula. t is just an indexer on values of x. Don't think we want to start changing it's definition based on n.
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8961b2 No.1736
>>1733
All is good, not posted much either since I'm little out of ideas and none of my attempts have gone anywhere. Still here banging my head against the grid with you!
Pretty sure I solved it in a dream already but not sure how. Doh.
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a92e07 No.1737
>>1735
I was having a really hard time with understanding what VQC meant when he said:
>At the correct element in the grid at (e,1) where the value of a at that element equals the na we want, if you subtract 2d+1 from na then you are in the negative half of the grid in terms of e and the value at the same element in the first row will be (n-1)a
I believe the "na" that we want refers to the na in the 2na = x^2 + e.
This is why I think the equation is important.
I'm trying to work out what the (n-1)a cell means now.
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537a7c No.1738
>>1733
Teach! Nice to see you!
>>1736
Nice to see you too, Anon!
>>1735
Well, if we’re able to solve for the small square using the t equations in row one that’s great! How do we tie that together with the column 0 knowledge? Or is it needed? If we know c, d and the small square, are we back to solving for n with the quadratic we derived? Column 0 still needs to get tied in? Thoughts, Anons?
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ac6203 No.1739
>>1737
Teach - likewise. I'm not sure I fully understand, but here's where my head is by way of an example:
c=145
1 x c => (1,61,6) = {1:61:12:11:1:145} = 145; (x+n)^2=72x72=5184; (d+n)^2=73x73=5329;
1 x c na => (1,1,6) = {1:1:72:11:61:85} = 5185; (x+n)^2=12x12=144; (d+n)^2=73x73=5329;
In the first record, calculate (n-1)*a = (61-1)*1 = 60.
If you look at the differences in the n, d, and a values between (1,61,6) and (1,1,6) you will notice:
n = 1
d = d + 60
a = a + 60
So essentially the amount you take off of n gets added into the d and a.
This "transform" enables us to move from any (e,n) into the (e,1) space, and explains what's happening to d and a along the way.
I have played with this attempting to take off different values from n. (n-2), 2(n-1), etc. Haven't had much luck there.
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537a7c No.1740
>>1733
Ah, nice Teach! There’s that clear relationship between n and x we’ve been looking for. Nice rewrite on the formula! We’ve been banging our heads on that for a while, I think you just made it crystal clear.
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