1. I found the last page and a half difficult to wrap my brain around. The first concept is the solutions to ax congruent to b mod n when the gcd(a,n) is not equal to 1. I think it is the relationship between the x is congruent to c mod m as a solution to ax congruent to b mod n. I just don't see how they relate.
The second concept is working with fractions. I can see the benefit when working with large numbers, but seems like a lot more work in the because you would have to know the multiplicative inverse or all the denominators one could divide by for the modulo.
2. Though the operations with congruences are somewhat difficult to get a wrap around, I find it the most interesting. Congruences are now more than just an interesting fact using remainders. It will be interesting to see how these are applied.
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