assignment6

# A prove that for any given n this relationship is an

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Unformatted text preview: pairs of natural numbers. Problem 6 5 For any positive integer, we define a relation on all the integers called “congruence mod n”. Two integers a and b are “congruent mod n” if the both have the same remainder when divided by n (or stating it another way, if n divides (a b)).  ­a ­ Prove that for any given n, this relationship is an equivalence relation.  ­b ­ For a given n, prove that every integer is congruent mod n to one of the following numbers: 0, 1, …, n ­1. Problem 6 6 FACT: We will prove in class that if a is congruent to a’ and b is congruent to b’ mod n, then a+b i...
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## This note was uploaded on 01/29/2014 for the course MATH 300A taught by Professor Jamesking during the Winter '11 term at University of Washington.

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