Two right isosceles triangles of legs equal to $1$ are glued together to form either an isosceles triangle - called t-shape - of leg $\sqrt2$, or a parallelogram - called p-shape - of sides $1$ and $\sqrt2$. Find all integers $m$ and $n, m, n \ge 2$, such that a rectangle $m \times n$ can be tilled with t-shapes and p-shapes.
Problem
Source: 2017 Romania JBMO TST 1.4
Tags: combinatorics, combinatorial geometry, tiles, Tiling
