Hugo Mills on Nostr: It's a *system* of linear equations, not just a single one, and it's over the natural ...

It's a *system* of linear equations, not just a single one, and it's over the natural numbers not the integers, which complicates things. This is why I've got vectors on both sides of the equation, because I can't guarantee to be able subtract numbers.

There are definitely cases which have no non-trivial solutions:

u_1 = (1, 0), v_1 = (0, 1).

The only solution to this is x_1 = y_1 = 0.