For me, it was rather difficult to piece together the Chinese remainder theorem. It took me a little while to understand, and I still do not quite get how it all works together. The part that I am most struggling with is the a^(-1)b as being a solution. I suppose that it has to do that you are trying to find something congruent to this? I understood the method better through the examples, but still not the theory.
I did like the method for solving the ax+b equations. I remember that we covered that a little bit in Cryptography class, so that was nothing too new. I feel that I understand that part all right.
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