We can express modular arithmetic with the following equation:a = qm +r wherea = dividend and - o < a < 00q = quotient and - o 0r = remainder and 0

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1. Find the value for q given: (a) 39 = 4( mod 5) (b) -43 = 1( mod 4)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 90E

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Question

We can express modular arithmetic with the following equation:
a = qm +r where
a = dividend and - o < a < 00
q = quotient and - o <q<0
m = mod and m >0
r = remainder and 0 <r<m
We can use the above equation to help us solve modular arithmetic problems in which we want to find the
remainder of various mumbers by finding the congruencies.
1. Find the value for q given:
(a) 39 = 4( mod 5)
(b) -43 = 1( mod 4)
2. Check to see if the congruence are true using the below definition. Please show your work.
Definition. (Congruence Mod n) a = b( mod n) if and only if n | (a – b) if and only if n divides
(a – b) if and only if (a – b) is a multiple of n.
(a) 26 = 2( mod 4)
(b) 17 = 1( mod 4)
(c) 3500250010 = 1000200005( mod 5)
Lemma. if a = b( mod n) and if e= d( mod n) then ač = bd( mod n).

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