If $n>k$, $n \mid km$, and $m \nmid n$, does this imply that $k \mid n$? I think I am missing something very obvious here, but I've got the following question:


  Be $k,m,n \in \mathbb{Z}$ with $n \ge m$, $n &gt; k$, $n \mid k \cdot m$ and $m \nmid n$


Does this imply $k \mid n$?
No. For a counterexample, you can take $k = 6, m = 10$, and $n = 15$.

It is possible you are misremembering the following similar statement.

If $a \mid bc$ and $\gcd(a,b) = 1$, then $a \mid c$. This is stated and proved on MSE elsewhere.
the statement shows us that $k*m = r*n$ for some $r$. if $gcd(k,r) = d$, $d &gt; 1$and $d$ doesn't divide $n$, then clearly $k$ doesn't divide $n$