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