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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 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
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)).
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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