This is an amazing exposition of Tonelli-Shanks! (or at least something equivalent to it) I've always known that it exists, but I've always found it opaque and unmotivated (hence I've always preferred Cipolla's algorithm), but this lecture makes it seem very natural, like I could have come up with it! Well, I still think Cipolla's algorithm is easier to remember and understand, but I'm glad Tonelli-Shanks is also understandable now! Note: we don't need to use 2^k s + nt = 1. We can just use 2s + nt = 1 and the algorithm still works. But the latter is better since there's an easy solution: s = (n+1)/2 and t = -1. Thanks for the great lecture!
I thought I will just watch for a few minutes... Well I was mesmerized and watched the whole video!! He's a wizard
This is an amazing exposition of Tonelli-Shanks! (or at least something equivalent to it) I've always known that it exists, but I've always found it opaque and unmotivated (hence I've always preferred Cipolla's algorithm), but this lecture makes it seem very natural, like I could have come up with it!
Well, I still think Cipolla's algorithm is easier to remember and understand, but I'm glad Tonelli-Shanks is also understandable now!
Note: we don't need to use 2^k s + nt = 1. We can just use 2s + nt = 1 and the algorithm still works. But the latter is better since there's an easy solution: s = (n+1)/2 and t = -1.
Thanks for the great lecture!
can't believe these don't have more views
Thank you
yeee
this is so hard holy