Let p, q, and r be prime natural numbers with p # q and n= p2q. Then, all the subfields of GF(r") are a) GF(r4) for d=1, p, and q. b) GF(rd) for d = 1,p,q and pq. c) GF(r") for d = 1,p,q.pq,p² and p'q. d) GF(r4) for d = 1,p.p².q.r.pq.pr.qr.pqr, and p q. O a) O b) O c) d)
Let p, q, and r be prime natural numbers with p # q and n= p2q. Then, all the subfields of GF(r") are a) GF(r4) for d=1, p, and q. b) GF(rd) for d = 1,p,q and pq. c) GF(r") for d = 1,p,q.pq,p² and p'q. d) GF(r4) for d = 1,p.p².q.r.pq.pr.qr.pqr, and p q. O a) O b) O c) d)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let p, q, and r be prime natural numbers with p # q and n = p²q. Then, all the
subfields of GF(r") are
a) GF(r4) for d=1, p, and q.
b) GF(rd) for d = 1,p,q and pq.
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c) GF(r") for d = 1,p,q.pq.p² and p2q.
d) GF(r") for d = 1,p.p,q,r.pq.pr, qr.pqr, and p2q.
a)
b)
O d)
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