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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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