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(1 point) This question concerns the field GF(16). The modulus is P(x) = x² + x + 1. Please answer the following questions about arithmetic in this field. a) If p(x) = x³, what is p¹ (x) modulo P? b) If p(x) = x², what is p¹ (x) modulo P? c) If p(x) = x³ = x² + x² + 1, what is p−1 (x) modulo P? -1 d) If p(x) = x³ + x² + x + 1, what is p¯¹ (x) modulo P? Hint: The inverse of each polynomial appears in another sub-part of the question

(1 point) This question concerns the field GF(16). The modulus is P(x) = x² + x + 1. Please answer the following questions about arithmetic in this field. a) If p(x) = x³, what is p¹ (x) modulo P? b) If p(x) = x², what is p¹ (x) modulo P? c) If p(x) = x³ = x² + x² + 1, what is p−1 (x) modulo P? -1 d) If p(x) = x³ + x² + x + 1, what is p¯¹ (x) modulo P? Hint: The inverse of each polynomial appears in another sub-part of the question

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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(1 point) This question concerns the field GF(16). The modulus is P(x) = x² + x + 1. Please answer the following questions about arithmetic in this field. a) If p(x) = x³, what is p¹ (x) modulo P? b) If p(x) = x², what is p¹ (x) modulo P? c) If p(x) = x³ = x² + x² + 1, what is p−1 (x) modulo P? -1 d) If p(x) = x³ + x² + x + 1, what is p¯¹ (x) modulo P? Hint: The inverse of each polynomial appears in another sub-part of the question
Transcribed Image Text:(1 point) This question concerns the field GF(16). The modulus is P(x) = x² + x + 1. Please answer the following questions about arithmetic in this field. a) If p(x) = x³, what is p¹ (x) modulo P? b) If p(x) = x², what is p¹ (x) modulo P? c) If p(x) = x³ = x² + x² + 1, what is p−1 (x) modulo P? -1 d) If p(x) = x³ + x² + x + 1, what is p¯¹ (x) modulo P? Hint: The inverse of each polynomial appears in another sub-part of the question
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