Dissection of Rectangle into 9 Distinct Integral Squares

Theorem
Let $R$ be a rectangle.

Let $R$ be divided into $n$ squares which all have different lengths of sides.

Then $n \ge 9$.

The smallest rectangle with integer sides that can be so divided into squares with integer sides is $32 \times 33$.


 * RectangleDissectedInto9Squares.png