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knowLittle
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Homework Statement
a.) Prove: If an integer ##a## does not divide ##bc##, then ##a## does not divide ##b## and ##a## does not divide ##c##.
b.) State and either prove or disprove the converse of the above statement.
The Attempt at a Solution
a.) Proof by contrapositive
## a|c \vee a|b \implies a|bc \\ c=ak \vee b =ap ##Now, we multiply them by each other and
## bc = a(kap) , kap \in \mathbb{Z} ##
So, it follows and the original statement in a is proved.
b.) Now, the converse.
## a\not|c \wedge a\not |b \implies a \not | bc ##Can I say?
## a\not|c \wedge a\not |b ##
## c \not =ak \\ b \not = ap ##Multiply
##cb \not = a(kap) ## then
## a \not | cb, kap \in \mathbb{Z}##