If you could help with some hints there are two I'm wondering about.
What has a[p + 1 - t] have to do with the solution (or a solution?) and the other hint about
at the correct a[t], d[t] - d = a(n-1). How would those fit in with a solution?
Yes, it helps a lot.
This is my take on it too. Which then complements >>9881. We can use superpositions because they are the same object, just from different perspectives.
We're only given one perspective and what we're trying to do is to warp it to an equal, but different perspective so we can see the the whole object.
If you think of it in terms of complex numbers, then we can think of it as we're missing the lateral piece (also known as the imaginary part).
If you think of d+n as the real part and x+n as the lateral part, then our c is missing a piece. Take ((d+n) + (x+n)i)*( (d+n) + (x+n)i) and you will get c + lateral i. But our starting point is just c. We're missing the lateral part of our number, meaning we only hold a piece of the information. By finding d+n, x+n we have enough information to recreate the lateral part.
I thought it might be something like the above a while ago and did some naive testing. The only complex square roots of c + ki (for some k 0) are …. (d+n) + (x+n)i (with non-exhausting testing so I might wrong).
For a c with more than two factors we will have multiple valid (d+n, x+n) pairs. One for each factor (including 1, c).
I think I'm on board. At least with the grander idea. What does the rate of change mean in the context of the grid?