A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which the squares need not be different sizes are called Mrs. Perkins's quilts. If no subset of the squares forms a rectangle, then the perfect square is called "simple." Perfect square dissections correspond to square numbers which are the sum of square numbers. The simplest place to look for such a square might therefore be thought to be square pyramidal numbers.
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