() 2p n! (a) (") = 2 (mod p), where k for 0

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 30E: 30. Prove statement of Theorem : for all integers .
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Prove the congruence
2p
(a)
()
n!
= 2 (mod p), where
k
k!(n – k)!
for 0 <k < n.
(b) (Зр — 1)! 2р2 (mod p3)
Transcribed Image Text:2p (a) () n! = 2 (mod p), where k k!(n – k)! for 0 <k < n. (b) (Зр — 1)! 2р2 (mod p3)
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