a) If p(x) = x² + x² + s ²+x+1, and g(x) = x² + : b) If p(x) = x² + x³ + x² + x + 1, and g(x) = x² + x¹ + x² + 1, what is p(x)/q(x)? + x + 1, what is p(x)/q(x)?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**GF(256) Arithmetic Problems**

This question concerns the field \(GF(256)\). The modulus is \(P(x) = x^8 + x^4 + x^3 + x + 1\).

*For computing inverses in this field, you should use the table in the textbook.*

Please answer the following questions about arithmetic in this field.

a) If \(p(x) = x^7 + x^4 + x^2 + x + 1\), and \(q(x) = x^7 + x^5 + x^4 + x^3 + x^2 + x + 1\), what is \(p(x)/q(x)\)?

\[ \text{[Answer box here]} \]

b) If \(p(x) = x^4 + x^3 + x^2 + x + 1\), and \(q(x) = x^7 + x^4 + x^2 + 1\), what is \(p(x)/q(x)\)?

\[ \text{[Answer box here]} \]
Transcribed Image Text:**GF(256) Arithmetic Problems** This question concerns the field \(GF(256)\). The modulus is \(P(x) = x^8 + x^4 + x^3 + x + 1\). *For computing inverses in this field, you should use the table in the textbook.* Please answer the following questions about arithmetic in this field. a) If \(p(x) = x^7 + x^4 + x^2 + x + 1\), and \(q(x) = x^7 + x^5 + x^4 + x^3 + x^2 + x + 1\), what is \(p(x)/q(x)\)? \[ \text{[Answer box here]} \] b) If \(p(x) = x^4 + x^3 + x^2 + x + 1\), and \(q(x) = x^7 + x^4 + x^2 + 1\), what is \(p(x)/q(x)\)? \[ \text{[Answer box here]} \]
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