Hello lads! Working and thinking over here. I have a few good new ideas, just working on testing them first. Thinking on the (x+n) square and this:
>Then fill the square with n0^2 and multiples of 2d.
I'm thinking of n0^2 as little squares inside the bigger (x+n) square. Like doing a block puzzle with n0^2 pieces and 2d sized pieces. Or maybe 2d(n0-1) pieces?
Hello PMA! I'll start working on smaller examples of this:
>Breaking the problem down.
>First by roots.
>Then by triangular numbers.
I think that the "levels" of each root and remainder could be helpful in eliminating unnecessary calcs. Maybe our desired (x+n) is 1) a multiple of the lowest levels of the factor tree (or GCD) and 2) a triangular number. Process of elimination. Maybe the factor tree aids in more efficient searching, not providing an answer up front.
>If there was some way we could turn every operation into a small n value search, then I think we would have our solution
This is where the (e,1) connection has to come in. Row 1 is the “one row to rule them all.”