In your solution you assert that 2M-N and 2M+N are both squares, namely a^2 and b^2. How do account for the fact that it is possible for the quotient (2M-N)/(2M+N) to be a rational square but not 2M-N and 2M+N individually? [For example M=5, N=8 yields (2M-N)/(2M+N) = (10-8)/(10+8) = 2/18 = 1/9 = (1/3)^2].