Divide a positive number, say 20, into a sum of two positive rational numbers x, y such that for some positive rational number z both z² + x and z2 + y are squares (of rational numbers). For the sake...

Extracted text: Divide a positive number, say 20, into a sum of two positive rational numbers x, y such that for some positive rational number z both z² + x and z2 + y are squares (of rational numbers). For the sake of definiteness, write z? + x = (z+ 2)² and z² + y = (z +3)².