Let p be a prime number. Prove that for all nonzero a € Zp, z-a is a divisor of r²-1-1 in Zp[r]. Hence, we must have 2-1 p-1 -1= II(x-a) a=1 in Zp[r].
Let p be a prime number. Prove that for all nonzero a € Zp, z-a is a divisor of r²-1-1 in Zp[r]. Hence, we must have 2-1 p-1 -1= II(x-a) a=1 in Zp[r].
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.6: Congruence Classes
Problem 18E
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![Let p be a prime number. Prove that for all nonzero a € Zp, z-a is a divisor of r²-1-1 in Zp[r]. Hence, we must have
p-1
2-1
-1= II(x-a)
a=1
in Zp[r].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ee5f10d-8e0f-4b5f-b908-63d5f1db8707%2F7223704e-3d93-4523-8b23-b7f512b8e7c5%2Fjp0407a_processed.png&w=3840&q=75)
Transcribed Image Text:Let p be a prime number. Prove that for all nonzero a € Zp, z-a is a divisor of r²-1-1 in Zp[r]. Hence, we must have
p-1
2-1
-1= II(x-a)
a=1
in Zp[r].
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