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 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