*All* the solutions to a² + b² = c². How did the Babylonians solve it?

The math behind solving all the Pythagorean triples, a²+b²=c² and the story of the Plimpton 322 clay tablet which shows the Babylonians knew this 3800 years ago, about 1000 years before Pythagoras.

Timestamps:
0:00 Let's Learn Everything podcast line
3:01 Solution using the binomial (x+y)²
8:15 On the Babylonian tablet Plimpton 322
14:26 Errors on the tablet
17:22 How did the Babylonian number system work

Link to the Let's Learn Everything Podcast I mentioned:
https://maximumfun.org/episodes/lets-...

Text Sources:
Wikipedia page. great starting point, some things were a bit unclear here and some details, like error in row 8, not discussed in detail.
https://en.wikipedia.org/wiki/Plimpto...

Great modern Review article with discussion on all the classical theories, my main source.
Britton, John P.; Proust, Christine; Shnider, Steve (2011), "Plimpton 322: a review and a different perspective", Archive for History of Exact Sciences, 65 (5): 519–566 https://doi.org/10.1007%2Fs00407-011-...

Beautiful hand drawn pictures and discussion in a math journal
Robson, Eleanor (February 2002), "Words and pictures: new light on Plimpton 322" , American Mathematical Monthly, 109 (2), https://doi.org/10.2307%2F2695324

Newest paper that claims relationship to trigonometric tables
Mansfield, Daniel F., and Norman J. Wildberger. “Plimpton 322 Is Babylonian Exact Sexagesimal Trigonometry.” Historia Mathematica 44, no. 4 (2017): 395–419. https://doi.org/10.1016/j.hm.2017.08.001 see also their related video here
   • Old Babylonian mathematics and Plimpton 32...  

UBC course website on Plimpton, also really great!
https://personal.math.ubc.ca/~cass/co...

Video links:
3Blue1Brown’s exposition using complex numbers (and super pretty argument that we’ve got them all) “All possible pythagorean triples, visualized”    • All possible pythagorean triples, visualized  

Numberphile video on how the Babylonians wrote in clay tablets
"Cuneiform Numbers - Numberphile"    • Cuneiform Numbers - Numberphile  

Jim Simon's video about place values in the Babyonian writing
"Babylonian Mathematics"    • Babylonian Mathematics  

Image credits:
Plimpton 322 tablet from https://commons.wikimedia.org/wiki/Fi... "public domain because of age"

Edgar J Banks https://commons.wikimedia.org/wiki/Fi... From 1922, public domain.