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Syrus
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Homework Statement
Prove that for every integer n, 15|n iff 5|n and 3|n.
I have proven the "if" direction. My question regards the "only if" portion of the proof.
So far I have:
(<--) Suppose 5|n and 3|n. Then there are j,k ∈ Z for which n = 5j and n = 3k.
*above, Z stands for the set of integers
I have found that both (j + k)/8 and (j - k)/2 seem to provide the desired value to show that 15|n, however I am not entirely sure how to show that either of these values is an integer (as is required by the definition of "divides"). I assume I am not proposing a clever enough value (or form) for the divisor. Any advice on this?