MATH135 Study Guide - Final Guide: Dnv Gl, Modular Arithmetic

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Mike Eden

Document Summary

If a, b z we say that a is congruent to b modulo m, and write a b (mod m) if m|j (a - b). If m (a - b), we write a 6(not) b (mod m). Then: a a (mod m). (reflexivity, if a b (mod m), then b a (mod m). (symmetry, if a b (mod m) and b c (mod m), then a c (mod m). (transitivity) If a a0 (mod m) and b b0 (mod m), then: a + b a0 + b0 (mod m, a - b a0 + b0 (mod m, ab a0b0 (mod m) If ac bc (mod m) and gcd(c, m) = 1, then a b (mod m). Proposition (congruent i_ same remainder (cisr)) a b (mod m) if and only if a and b have the same remainder when divided by m. Identity is an element e s so that for all a s, a (an operation) e =a.