give-a-b-c-gt-0-if-a-b-and-b-c-prove-a-c-

Question Number 73553 by 01 last updated on 13/Nov/19

give : a, b, c > 0

if a ∣ b and b ∣ c

prove : a ∣ c

Answered by Rio Michael last updated on 13/Nov/19

a ∣ b \Leftrightarrow \exists k \in Z : b = k a \dots \dots (i)

b ∣ c \Leftrightarrow \exists m \in Z : c = b m \dots . . (i i)

e q n (i) i n (i i) \Rightarrow

c = (k a) m

c = k m a

i f k, m \in Z t h e k m \in Z

h e n c e a ∣ c