I think that it is interesting looking at nonlinear congruences. When x-squared is congruent to 1, it is basically solving for which numbers are their own inverses. The book said that for all odd primes plus or minus 1 mod p are the only solutions. I would like to know if there are similar results for x-cubed and so on.
I think that solving modular equations was the part that was most difficult in these sections. I never remember that they are a lot easier to solve once you have done the extended Euclidean Algorithm.
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