Double Squares

 The Problem:

The number 65 can be written as the sum of two squares:                     65 = 42 + 72

Can you write its double, 130, in a similar way? 

Try a few more like this:                   34 = 52 + 32

Does                                                  68 = a2 + b2 , for some whole numbers a and b? 

What about   58  and  500, which are the doubles of    29 = 22 + 52  and  250 = 92 + 132 ?

 

Can you find a pattern in how to write the doubles as the sum of two squares?  

Can you prove your method will always work?

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Last modified: June 18, 2007