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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? |
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