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
icon
Related questions
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
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
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,