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Unformatted text preview: Math 4383 Section 4.2 Extra Page 1 of 5 Number Theory Chapter 4 Section 4.2 – Extra Information on Congruence Any set of n integers that are incongruent modulo n is called a complete set of residues mod n. The “standard” set is the set of numbers 0,1,2,…, n1. For every integer k, define the congruence class of k mod n by ( 29 [ ] { : mod } k x x k n = ≡ Remember that congruence is an equivalence relation – which means that [k] = [x] if and only if ( 29 mod k x n ≡ THE SETS ARE THE SAME!!!! If we look at all the congruence classes mod n for all the integers, there are only n distinct sets. These can be represented as the congruence classes of 0, 1, 2, 3, … , n1 Consider the SET where each element is a distinct congruence class mod n. For each distinct set, we use the integer k between 0 and n1 which is contained in the set as the representative member Call this set “Z n” { } [0],[1],[2],...,[ 1] n n = ℤ Operations corresponding the addition and multiplication are defined by...
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This note was uploaded on 02/21/2012 for the course MATH 4383 taught by Professor Flagg during the Spring '09 term at University of Houston.
 Spring '09
 flagg
 Number Theory, Congruence, Integers

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