I ran large searches on Euler bricks — interesting modular obstruction patterns (mod 19) Hi everyone, I’ve been exploring the perfect cuboid problem computationally and wanted to share some observations and get feedback. Quick recap: a perfect cuboid would be a box with integer edges (a, b, c) where all three face diagonals AND the space diagonal are integers. No example is known. In my experiments, I focused on two things: 1. Modular constraints (mod 19) I computed: S = a\^2 + b\^2 + c\^2 For a perfect cuboid, S would have to be a perfect square. Looking at S mod 19, squares modulo 19 can only be: 0, 1, 4, 5, 6, 7, 9, 11, 16, 17 So if S mod 19 is NOT one of those values, it can’t be a perfect square → meaning that Euler brick can’t be extended to a perfect cuboid. I found that many Euler bricks get eliminated immediately this way. However, this is not a complete obstruction. Some examples still pass (for example, one case gives S ≡ 17 mod 19). 2.…