Prove that a positive integer n is the sum of two perfect squares if and only if 2*n is also the sum of two perfect squares.
(In reply to
solution by Paul)
Nicely done, Paul. That proves the "only if" part.
All that is necessary to prove the "if" part is to point out that 2n is always even, so if 2n is the sum of two squares it can always be expressed as 2n = (2i + k)^2 + k^2. Then, as Paul has shown
with a little algebra, n = i^2 and (i+k)^2. q.e.d.
re: solution
