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).
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).
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 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...
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