"If we find a prime $p$ such that $p\mid n$ , then $n/p$ is a positive integer that's smaller than $n$."
I understand $n/p$ is $n$ divided by $p$ but what is $n\mid p$?
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For nonzero integers $x$ and $y$, the following are equivalent statements:
$x$ divides $y$
$x\mid y~~~~~~~~~~~~$(this is read aloud the same way as the previous line)
$y$ is divisible by $x$
$y\equiv 0\pmod{x}$
$\frac{y}{x}$ is an integer
There exists some integer $k$ for which $xk = y$
$y$ is a multiple of $x$
$x$ is a factor of $y$
On the other hand, $x/y$ is in this context another way of writing the fraction $\frac{x}{y}$
JMoravitz
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1"$y/x$ is an integer" is only equivalent if $x \ne 0$ (unless for some reason you want to throw out the case $0\mid 0$). – Jul 20 '16 at 19:24
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The expression "$n/p$" represents the number that you get when you divide $n$ by $p$, whereas the expression "$p\mid n$" represents the statement that $p$ divides evenly into $n$.
Oscar Cunningham
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vertical bar math notationgave me exactly what I needed, the first page (Wiki) being somewhat more difficult to find the needed information but the second result being exactly what is needed. Regardless, many people cannot Google effectively, and that seems to be the issue more than anything. Oddly, I think the context here, more than anything, should have pointed OP in the right direction. – Daniel W. Farlow Jul 21 '16 at 00:52This question does not show any research effort; it is unclear or not useful.As far as I'm concerned, the question showed no research effort, and I should not feel like I have to justify every single downvote I give (I find it rather priggish of you to judge anyone's "silent downvote" as inappropriate). Have you left 57 comments for the downvotes you have given? The question concerning downvotes has been beaten to death on meta, and it is not a fruitful discussion to have. I suppose we shall simply have to agree to disagree here. – Daniel W. Farlow Jul 21 '16 at 02:08