obtained from f(x) by reducing all the coefficients of f(x) mo Assume that deg (f (x)) = deg(f(x)), then: If f (x) is reducible over Zp, then f (x) is reducible over Q If f(x) is irreducible over Zp, then f(x) is irreducible over Q If f(x) is reducible over Q, then f(x) is irreducible over Z., None of the above
obtained from f(x) by reducing all the coefficients of f(x) mo Assume that deg (f (x)) = deg(f(x)), then: If f (x) is reducible over Zp, then f (x) is reducible over Q If f(x) is irreducible over Zp, then f(x) is irreducible over Q If f(x) is reducible over Q, then f(x) is irreducible over Z., None of the above
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
number theory
![11. Let f (x) E Z[x] with deg (f(x)) 2 1. Let f (x) be the polynomial in Zp, p €
Z, obtained from f(x) by reducing all the coefficients of f (x) modulo p.
Assume that deg (f(x)) = deg(f(x)), then:
a) If f(x) is reducible over Zp, then f(x) is reducible over Q
b) If f(x) is irreducible over Zp, then f(x) is irreducible over Q
c) If f(x) is reducible over Q, then f(x) is irreducible over Z,
d) None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5eb63f2-3a06-45a0-8b80-8ebff6012d5c%2Fab083ac3-155e-422c-87a6-31936ee59591%2Fgciboqa_processed.png&w=3840&q=75)
Transcribed Image Text:11. Let f (x) E Z[x] with deg (f(x)) 2 1. Let f (x) be the polynomial in Zp, p €
Z, obtained from f(x) by reducing all the coefficients of f (x) modulo p.
Assume that deg (f(x)) = deg(f(x)), then:
a) If f(x) is reducible over Zp, then f(x) is reducible over Q
b) If f(x) is irreducible over Zp, then f(x) is irreducible over Q
c) If f(x) is reducible over Q, then f(x) is irreducible over Z,
d) None of the above
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