I found this which looks a little like you asked for:

The Babylonians were so advanced, they had a theorem for discovering Pythagorian triples.

If p and q take on all whole values subject only to the conditions

1) p > q > 0,
2) p and q have no common divisors other than 1,
3) p and q are not both odd,
then the expressions
x = p2 - q2,
y = 2pq
z = p2 + q2,
will produce all reduced Pythagorean number triples, and each triple only once. (Aaboe 30-31)

From:http://nova.bsuvc.bsu.edu/~00dbwolfe/paper.htm