The explanation of how to do the Chinese Remainder theorem in the book was difficult to follow. However the general form given at the end seemed to make more sense. I guess at the heart of it, it is basically the same thing as solving a system of equations in linear algebra, you just keep substituting up.
The proofs using congruences were quite nice, they are very simple but elegant. It also looks like congruences are pretty powerful even though there isn't much to them.
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