3. Let p= 37, and let f = 7-1. For each a in F,[r]/f, either find the inverse al or explain why the inverse does not exist. A computer program is needed for some (but not all) of these. (a) a = 8 (b) a=0 (c) a = r (d) a = x + 1 (e) a = 1 + 2 (f) a = 2²-1 Please solve as much as possible. If not please solve e, f, g, and h (g) a = r² + 1 (h) a=r³+²+1

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 12E: 12. Let and . For the given , decide whether is onto and whether it is one-to-one. Prove that your...
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3. Let p 37, and let f r – 1. For each a in F,r]/f, either find the inverse a- or explain
why the inverse does not exist. A computer program is needed for some (but not all) of these.
(a) a = 8
(c) a = r
(e) a = r+2
(g) a = r2 +1
(b) a 0
(d) a = r+1
(1) a = 2 -1
(h) a =
Please solve as much as possible. If not please solve e, f, g, and h
Transcribed Image Text:3. Let p 37, and let f r – 1. For each a in F,r]/f, either find the inverse a- or explain why the inverse does not exist. A computer program is needed for some (but not all) of these. (a) a = 8 (c) a = r (e) a = r+2 (g) a = r2 +1 (b) a 0 (d) a = r+1 (1) a = 2 -1 (h) a = Please solve as much as possible. If not please solve e, f, g, and h
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