ECE103 Midterm: Congruence

• School: University of Waterloo
• Department: Electrical and Computer Engineering
• Course: ECE103
• Professor: Martin Pei

Document Summary

Definition 3. 1. 1 for any integers a, b, and m, m > 0, we say that a is congruent to b modulo m, and write a b (modm) if m|(a b). If m |(a b), we say that a is not congruent to b modulo m and write a b (mod m). Modulo: let a, b and m be integers, m > 0. There is an integer q such that a = b+mq if and only if a b (mod m). The next theorem establishes three important properties of congruence modulo m. If a a (mod m) and b b (mod m), then, by proposition 4, there exist integers p and q such that a = a +pm and b = b +qm. +pm)+(b +qm) = (a +b )+(p+q)m. since p+q is an integer, proposition 3. 1. 4 implies a+b a +b (mod m).