a) If a| (21b−c) and 6c≅3b(mod2a), then a| 41c b) If a≅b(modc) and d|c then ?≅?(mod?) c) ∴(d| (ab+c) & d| b) <--> (d| b & d| c)

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 30E: 30. Prove that any positive integer is congruent to its units digit modulo .
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Assume a,b,c are integers. Prove the following.

a) If a| (21b−c) and 6c≅3b(mod2a), then a| 41c

b) If a≅b(modc) and d|c then ?≅?(mod?)

c) ∴(d| (ab+c) & d| b) <--> (d| b & d| c)

 

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