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.
Has this problem changed? The first time I looked, I the
problem talked about two perfect squares. Now it says two
perfect "nonzero" squares, which is what I assumed anyhow, but Jer and
K Sengupta assumed otherwise.
The first two solutions start by proving the case for n = 2. This
doesn't work for the revised problem. For example, if P = 2 and
Q = 2, then they are each the sum of two positive squared
integers. But their product, 4, is not the sum of two positive
squared integers.
So, the proof for n = 3 cannot be proved by
first proving n = 2, al least not now that the problem has been made
more pointed (and interesting).
Edited on May 19, 2007, 1:06 pm
Not so fast!
