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For each of the questions below, answer "always,” “sometimes,” or “never,” then explain your answer. Your explanation should justify why you chose the answer you did, but does not have to be a rigorous proof. Hint: Recall that if a = b (mod m) then there exists an integer k such that a = b+mk. (a) Suppose a = 2 (mod 21). When is a = 2 (mod 7)? (b) Suppose b = 2 (mod 7). When is b = 2 (mod 21)? (c) Suppose c = 5 (mod 8). When is c = 4 (mod 16)? (d) Suppose d = 3 (mod 21). When is d = 0 (mod 6)?

For each of the questions below, answer "always,” “sometimes,” or “never,” then explain your answer. Your explanation should justify why you chose the answer you did, but does not have to be a rigorous proof. Hint: Recall that if a = b (mod m) then there exists an integer k such that a = b+mk. (a) Suppose a = 2 (mod 21). When is a = 2 (mod 7)? (b) Suppose b = 2 (mod 7). When is b = 2 (mod 21)? (c) Suppose c = 5 (mod 8). When is c = 4 (mod 16)? (d) Suppose d = 3 (mod 21). When is d = 0 (mod 6)?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 34E
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For each of the questions below, answer "always," "sometimes," or "never," then explain your answer. Your explanation should justify why you chose the answer you did, but does not have to be a rigorous proof. Hint: Recall that if a = b (mod m) then there exists an integer k such that a = b+mk. (a) Suppose a = 2 (mod 21). When is a = 2 (mod 7)? (b) Suppose b = 2 (mod 7). When is 6 = 2 (mod 21)? (c) Suppose c = 5 (mod 8). When is c = 4 (mod 16)? (d) Suppose d = 3 (mod 21). When is d = 0 (mod 6)?
Transcribed Image Text:For each of the questions below, answer "always," "sometimes," or "never," then explain your answer. Your explanation should justify why you chose the answer you did, but does not have to be a rigorous proof. Hint: Recall that if a = b (mod m) then there exists an integer k such that a = b+mk. (a) Suppose a = 2 (mod 21). When is a = 2 (mod 7)? (b) Suppose b = 2 (mod 7). When is 6 = 2 (mod 21)? (c) Suppose c = 5 (mod 8). When is c = 4 (mod 16)? (d) Suppose d = 3 (mod 21). When is d = 0 (mod 6)?
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