The polynomial is irreducible over Z5. (Do NOT show this.) Let a be a zero of f(x) in some extension field of Z5. 4 f(x) = x² + x² + 2 € Z5[x] Write a as a linear combination in the basis {1, a, a², a³} for Z5(a) over Z5 and show that a ¹0-a² - 1.
The polynomial is irreducible over Z5. (Do NOT show this.) Let a be a zero of f(x) in some extension field of Z5. 4 f(x) = x² + x² + 2 € Z5[x] Write a as a linear combination in the basis {1, a, a², a³} for Z5(a) over Z5 and show that a ¹0-a² - 1.
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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![The polynomial
is irreducible over Z5. (Do NOT show this.) Let a be a zero of f(x) in some extension
field of Z5.
= x² + x² + 2 € Z5 [x]
==
f(x) = x²
1
Write a-¹ as a linear combination in the basis {1, a, a², a³} for Z5(a) over Z5 and show
that a ¹0 -a² - 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09c2f836-a777-444b-9271-94b360db7692%2F679452c3-f2a5-4cdb-ac4e-fc1cb7966e52%2Fj6dd5qn_processed.png&w=3840&q=75)
Transcribed Image Text:The polynomial
is irreducible over Z5. (Do NOT show this.) Let a be a zero of f(x) in some extension
field of Z5.
= x² + x² + 2 € Z5 [x]
==
f(x) = x²
1
Write a-¹ as a linear combination in the basis {1, a, a², a³} for Z5(a) over Z5 and show
that a ¹0 -a² - 1.
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