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Question 6. Given integers a, b, c, d € Z, and m, n € N. (a) Suppose that a = b (mod n), and that m | n. Prove that a = b (mod m). (b) Prove or disprove: a³ = a (mod 3). (c) Suppose that a = b (mod n) and c= d (mod n) prove that a+c=b+d (mod n).

Question 6. Given integers a, b, c, d € Z, and m, n € N. (a) Suppose that a = b (mod n), and that m | n. Prove that a = b (mod m). (b) Prove or disprove: a³ = a (mod 3). (c) Suppose that a = b (mod n) and c= d (mod n) prove that a+c=b+d (mod n).

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 29E: 29. Find the least positive integer that is congruent to the given sum, product, or power. a. ...
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Question 6. L Given integers a, b, c, d e Z, and m, n € N. (a) Suppose that a = b (mod n), and that m | n. Prove that a = b (mod m). (b) Prove or disprove: a³ = a (mod 3). (c) Suppose that a = b (mod n) and c= d (mod n) prove that a+c=b+d (modn).
Transcribed Image Text:Question 6. L Given integers a, b, c, d e Z, and m, n € N. (a) Suppose that a = b (mod n), and that m | n. Prove that a = b (mod m). (b) Prove or disprove: a³ = a (mod 3). (c) Suppose that a = b (mod n) and c= d (mod n) prove that a+c=b+d (modn).
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