This assignment was a little difficult in understanding why a would be equivalent to b (mod p) but a is also equivalent to -b (mod q) when a and b are square roots of some number modulo n. I understand how to use these facts, but I'm still a little shaky on why they work.
In looking at this section, I'm fascinated by the fact that these problems can have 4 square roots instead of the normal 2 we would expect. Modular arithmetic just always seems to be full of surprises.
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