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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)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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