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Subtle Summed Squares (Posted on 2007-05-18) Difficulty: 3 of 5
Suppose a number N can be written as P times Q times R times..., where all of P, Q, R... can each be written as the sum of two perfect nonzero squares.

Show that in this case N itself can also be written as the sum of two perfect squares.

See The Solution Submitted by Old Original Oskar!    
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re: Not so fast! | Comment 4 of 6 |
(In reply to Not so fast! by Steve Herman)

What seems to be a flaw at first is not.  The numbers P, Q, ... are expressable as the sum of non-zero squares.  The thing that was to be shown almost makes a point of not requiring the squares summing to N be non-zero.

If it did require the square summing to N be non-negative, then an exception occurs.  N cannot be a perfect square unless it is the square of a number that can be written as the sum of two squares in two different ways.

  Posted by Jer on 2007-05-21 12:26:28
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