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

re: Not so fast! by Jer)

And in fact it's a totally unneccessary condition, for if P, Q, R, and so on, are squares themselves (thus being zero squared plus itself) the formulas work out the same.