Hey AA! The diagram is the area of (x+n)^2. The two triangle numbers are represented by yellow (T2) and green (T1). The blue units are the remainders from (f-1) mod 8.
I think the key is adding the two bases of the staircase triangle numbers together, so in this case it's 4+3=7. For c6107, the correct u is 42. So in this example, 7 * 6 = 42. So the correct u value is a multiple of 7. In this case, u and u1 are 42 and 41, which add to 83, which is the correct x+n value. The correct area of this x+n square is 83^2 = 6889
I think the rm(2d-1) comes into play here by being able to give us a lock on the correct multiple of u that gives us a perfect square, 6889.
Here's the breakdown from VQC:
>The solution to this problem introduces a new form of algebra where two concurrent forms of equations run side by side and then merge.
>Take some time to think about what that means.
>Have you seen this approach before?
>What could it look like?
>Many new solutions often seem obvious in hindsight.
>In fact many new designs seem to simplify in many varied approaches to design.
>Does it seem obvious in hindsight that in order to solve a multivariate equation, that something new but similar to what we have always done, would be the solution? Just taken in a new direction? Expanded thinking.
>The two sets of equations take the problem and simplify it. Together they handle the "lock and key" nature of the problem/solution, particularly when c is divisible by 1, c, and two other prime numbers, such as in RSA.
>The two forms of equations that merge together handle staircase numbers where the base of one staircase, is one unit longer than the other.
>The analogy to Fermat's Last Theorem. Two objects that seem to be completely unrelated were proved to be the same object.
>Two seemingly different 'fields' will be used side by side and merged to create an elegant solution. Again, this can only be done in reverse, using the assumption that P=NP. I only saw at the end of over seven years work. Anons have got much further in six months than I would have. I would have walked away in frustration back in the day but you anons here have been amazing.
>Take some time to think what this will look like and how the diagrams (especially animated) might show this.
>I think things will start moving quickly.
>This will be new mathematics. It will make more sense than how this problem has been approached up until now.