Every square of integer length can be cut into a number of L's: .
For a pythagorean triple a^{2} + b^{2} = c^{2}, can the L's from an a x a square and a b x b square can be packed into a c x c square? The following pictures show that this is sometimes possible. There are 3 infinite families of packings illustrated below.
3^{2} + 4^{2} = 5^{2} 

5^{2} + 12^{2} = 13^{2} 

7^{2} + 24^{2} = 25^{2} 

4^{2} + 3^{2} = 5^{2} 

8^{2} + 15^{2} = 17^{2} 

12^{2} + 35^{2} = 37^{2} 

12^{2} + 5^{2} = 13^{2} 

28^{2} + 45^{2} = 53^{2} 

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Packing Page.