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(b) Showing your working, compute (5), Þ(23) and ¤(115).

(b) Showing your working, compute (5), Þ(23) and ¤(115).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 12E: a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant...
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(b) Showing your working, compute ¤(5), D(23) and ¤(115). (c) Let n = pq where p and q are two distinct primes. Recall that the Chinese Remainder Theorem states that there exists a one-to-one correspondence F between Zn and Z, x Z, such that F([0]n) = ([0]p, [0],) and F(1),) = ([1)p, [1]q). Give the function F for the case where n = 119, p = 7, q = 17 and compute the values F([25]119) and F-1([0]7, [1]17). Show your working!
Transcribed Image Text:(b) Showing your working, compute ¤(5), D(23) and ¤(115). (c) Let n = pq where p and q are two distinct primes. Recall that the Chinese Remainder Theorem states that there exists a one-to-one correspondence F between Zn and Z, x Z, such that F([0]n) = ([0]p, [0],) and F(1),) = ([1)p, [1]q). Give the function F for the case where n = 119, p = 7, q = 17 and compute the values F([25]119) and F-1([0]7, [1]17). Show your working!
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