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Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.6: Congruence Classes
Problem 25E
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O Prove or dis prove :If ab+c) then either alb or alc O Prove tha t for any integer a, one of the intgers 91972 at4 divis ble by 3. For an abitrary integer ai establis that 2 ala t1) while 31 a (at1) (at2) Prove that 4t ca?+2) for any integer a Prove albi7 and only if aclbc where c o 6) show that ifa is Gn integer SUch that and 3 a then 24 (a-1) 2X a Show that if and b.are integers with Caib) = 1 then (atb a-b) =lor 2 (3 sho w that if and b are integers that are not both zero,and c is anon zero int eger, then (ca, cb) -Icl Caib)
Transcribed Image Text:O Prove or dis prove :If ab+c) then either alb or alc O Prove tha t for any integer a, one of the intgers 91972 at4 divis ble by 3. For an abitrary integer ai establis that 2 ala t1) while 31 a (at1) (at2) Prove that 4t ca?+2) for any integer a Prove albi7 and only if aclbc where c o 6) show that ifa is Gn integer SUch that and 3 a then 24 (a-1) 2X a Show that if and b.are integers with Caib) = 1 then (atb a-b) =lor 2 (3 sho w that if and b are integers that are not both zero,and c is anon zero int eger, then (ca, cb) -Icl Caib)
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