Pythagorean Quadruples

Daniel Edgerton 15 Apr 2009 15:42

I had never even heard of these before, but after analyzing them, they seem to make sense.

A Pythagorean Quadruple is a set of integers s.t. $a^{2} + b^{2}+ c^{2} = d^{2}$.

Similarly Primitive Pythagorean Quadruples follow the same formula except that: (a,b,c,d) = 1 and

a = $m^{2} + n^{2} - p^{2} - q^{2}$

b = 2(mp + nq)

c = 2(np - nq)

d = $m^{2} + n^{2} + p^{2} + q^{2}$

where $m,n,o,p \in\mathbb{Z}$

If you want to check this out for yourself, there are a few examples at the website below.

http://en.wikipedia.org/wiki/Pythagorean_quadruple