1. Let p = 281. Given the following polynomials a and b in F,[r], use a computer program tocompute polynomials d, u, v in F, such that ged(a, b) = d = ua + vb. Python classes forworking with polynomial rings are given in the supplementary file polynom.py.(a) a = r5 – a? + 6x – 14b = 23 + 922 +x – 1(b) a = 26 + x5 – x* + 6a3 + 2x? – 5x + 10b = x7 + 25 + 2x4 – 2x3 + 6² – x + 2

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 11E: 11. a. Give an example of a ring of characteristic 4, and elements in such that b. Give an...

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