From many tablets it is clear that the Babylonian
mathematicians at least after circa 1900 BC knew the
Pythagorean theorem---and more than maybe 1400 years
before Pythagoras too
(Ne-35--36).
We don't know if they ever evolved a rigorous proof:
it seems unlikely---unlike Greek and modern
mathematicians such proofs don't seem to have interested
them.
But the Babylonians did investigate number properties it seems. A famous cuneiform tablet Plimpton 322 strongly suggests that they knew a general procedure for constructing Babylonian triples: i.e., three integers that satisfy the Pythagorean theorem (Ne-40). The tablet gives a demonstration of the procedure it seems: it doesn't give any directions. Plimpton 322 was first deciphered by O. Neugebauer and A. Sachs O. Mathematical Cuneiform Texts Amer. Oriental Series 29. American Oriental Society, New Haven, 1945.
I know of no verified public domain images of Plimpton 322 although unverified ones are at many sites. But Plimpton 322 is part of the Plimpton Collection of Columbia University and one is free to go to the Plimpton 322 page of Columbia's Collections & Treasures site.