11 Dec
2005
11 Dec
'05
4:02 p.m.
A Pythagorean triple is any integer solution of x^2+y^2=z^2 and, as we know, one gets all solutions by choosing any integers n>m. and defining T(m,n) by, x=n^2-m^2n, y=2mn, z=m^2+n^2.
<pedant>Not quite. You need to allow for a scaling factor on x,y,z too. Scaling m,n only lets you scale x,y,z by squares.</pedant> -- g