Section 5.1: Analysis

Congruence in and Congruence Classes

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This section takes all of the ideas of congruence and congruence classes from section 2.1 and demonstrates how it is valid in the field . The only visible adjustment is the definition of a residue class which essentially is the set of polynomials that leave a specific polynomial remainder when divided by another polynomial.

I wonder, however, how this can be useful, that is how is a residue class useful. It seems to be the equivalent of the remainder in after applying the division algorithm. If it is different how is it different? If it isn’t then why is it given a name other than ‘remainder polynomial’ or something along those lines.