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.
(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 nonzero squares. The thing that was to be shown almost makes a point of not requiring the squares summing to N be nonzero.
If it did require the square summing to N be nonnegative, 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 20070521 12:26:28 