Consider the polynomial ring Z9[x]. (a) For any positive integer k the polynomial 3xk + 1 is a unit in Z9[x]. What is its multiplicative inverse? (b) Write x ∈ Z9[x] as a product of two polynomials, each of positive degree.

Consider the polynomial ring Z9[x]. (a) For any positive integer k the polynomial 3xk + 1 is a unit in Z9[x]. What is its multiplicative inverse? (b) Write x ∈ Z9[x] as a product of two polynomials, each of positive degree.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the polynomial ring Z9[x].
(a) For any positive integer k the polynomial 3xk + 1 is a unit in Z9[x]. What is its
multiplicative inverse?
(b) Write x ∈ Z9[x] as a product of two polynomials, each of positive degree.

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