Question 155
Two right isosceles triangles of legs equal to $1$ are glued together to form either an isosceles triangle – called *t-shape* – of leg $\sqrt{2}$, or a parallelogram – called *p-shape* – of sides $1$ and $\sqrt{2}$. Find all integers $m$ and $n$, $m, n \ge 2$, such that a rectangle $m \times n$ can be tiled with t-shapes and p-shapes.