The hardest part for me was following what exactly was happening in the Chinese remainder theorem. Following why I need the inverse and what to do with it, was really hard for me to follow. For some reason when I tried to follow the various symbols I lost track, it was only when I was able to think of it more as picture that I was able to get it.
The most interesting part was the modular exponentiation. It is funny how easy such an efficient way of doing the exponentiation is.
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