10. We say that an integer a is nilpotent modulo m if there exists a pos- itive integer k such that a = 0 (mod m). Prove that a is nilpotent modulo m if and only if a = 0 (mod rad(m)).
10. We say that an integer a is nilpotent modulo m if there exists a pos- itive integer k such that a = 0 (mod m). Prove that a is nilpotent modulo m if and only if a = 0 (mod rad(m)).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 30E: 30. Prove that any positive integer is congruent to its units digit modulo .
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![10. We say that an integer a is nilpotent modulo m if there exists a pos-
itive integer k such that ak = 0 (mod m). Prove that a is nilpotent
modulo m if and only if a = 0 (mod rad(m)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30761ad5-6d22-4ff4-adb6-4f166a7ab52a%2F7c68046e-7eb2-46f3-a247-f4607a5908a9%2Fjxl5zq.jpeg&w=3840&q=75)
Transcribed Image Text:10. We say that an integer a is nilpotent modulo m if there exists a pos-
itive integer k such that ak = 0 (mod m). Prove that a is nilpotent
modulo m if and only if a = 0 (mod rad(m)).
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