I'm new to number theory. If we have a statement saying $n\mid91$, does it mean that $n$ can be $1, 7, 13, 91$, or n can be $7, 13$. Is $1$ and $91$ excluded?
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3It includes 1 and 91 – Aug 13 '19 at 11:18
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Aug 13 '19 at 11:20
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Thank you @MatthewDaly – user3980196 Aug 13 '19 at 11:20
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The bare statement $n\mid91$ does include the possibility that $n=1$ or $n=91$, since it is true that $1\mid91$ and $91\mid91$. Only if we said "$n$ is a non-trivial divisor of $91$" would $n=1,91$ be excluded from consideration.
Parcly Taxel
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"$x\mid y$" is shorthand for (or as we mathematicians say it, is defined as) "There is an integer $n$ such that $nx = y$". Nothing about $x\neq 1$ or $x\neq y$ in there. In fact, $1\mid y$ is always true, for any integer $y$, and I can imagine there are contest problems where this is used to show that some unknown number is indeed $1$.
This also means that we get $0\mid 0$, which isn't encountered often, but it's a fun little consequence that one might not consider.
Arthur
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