Just read In A primer of analytic number theory by Jeffrey Stopple, 2003 that there is a Babylonian cuneiform tablet (designated Plimpton 322 in the archives of Columbia University) from the nineteenth century b.c. that lists fifteen very large Pythagorean triples; for example, 127092^2 + 135002^2 = 185412^2.
This means that they must have known how to generate these numbers with
x = 2*s*t, y = s^2 − t^2, z = s^2 + t^2
For s=2,.t=1 we get the well known x=4, y=3, z=5 and
for s=3, t=1 we get 6, 8, 10 and
for s=4, t=2 we get 16, 12, 20.
1900 BC.
So 1900BC is much closer than I thought. The current blazing speed of scientic development has only been reacned since the last few hundred years or so.
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