Dissection of Rectangle into 9 Distinct Integral Squares

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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


Proof


Sources