The (5,16,19) divisibility conjecture

Prove that every equi-constructible side length X for the triangular tile with side lengths (5,16,19) is divisible by 16.

Background

The general divisibility conjecture is specialized in the paper to the tile (5,16,19), for which ab=80 but the conjectured necessary divisibility is stated as divisibility by 16. The authors identify this as the smallest interesting case of their broader conjecture.

References

As the smallest interesting case, we conjecture that all equi-constructible $X$ for $(5,16,19)$ are divisible by $16$.

— Tiling Triangles with $2π/3$ Angles  (2512.22696 - Zhang, 27 Dec 2025) in Conjecture 1, Section 3.1, Equilateral Triangles