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(d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

(d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

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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För each integer a, 3 divides a + 23a. 20. Are the following statements true or false? Either prove the statement is true or provide a counterexample to show it is false. (a) For all integers a and b, if a · b = 0 (mod 6), then a= 0 (mod 6) or b = 0 (mod 6). (b) For all integers a and b, if a · b = 0 (mod 8), then a = 0 (mod 8) or b = 0 (mod 8). (c) For all integers a and b, if a · b = 1 (mod 6), then a = 1 (mod 6) or b = 1 (mod 6). (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).
Transcribed Image Text:För each integer a, 3 divides a + 23a. 20. Are the following statements true or false? Either prove the statement is true or provide a counterexample to show it is false. (a) For all integers a and b, if a · b = 0 (mod 6), then a= 0 (mod 6) or b = 0 (mod 6). (b) For all integers a and b, if a · b = 0 (mod 8), then a = 0 (mod 8) or b = 0 (mod 8). (c) For all integers a and b, if a · b = 1 (mod 6), then a = 1 (mod 6) or b = 1 (mod 6). (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).
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