Absolute division symbol?

Asked Oct 07 '16 at 13:31

Active Oct 08 '16 at 11:46

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I am looking for a symbol "*" to mean "absolutely divides". For instance, by writing $$a^n*b$$ I mean $a^n\mid b$ but $a^{n+1}\nmid b$.

I remember I came across the symbol "$\parallel$" meaning this, but not sure if this is standard. I am not even sure if "absolutely divides" is a standard term for this meaning.

edited Oct 08 '16 at 11:46

Watson

23,793

asked Oct 07 '16 at 13:31

Easy

4,485

1

As a rule of thumb: if you can't think of the symbol for something, your reader won't recognize the symbol that you use so as long as you're consistent and clear with your definition of the symbol you'll be fine with whatever you use. – Jam Oct 07 '16 at 13:40
@Jam True. But if there is a convention of using some particular symbols, it is better for us to follow that. – Easy Oct 07 '16 at 13:47
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I think $||$ is standard. In my head it reads "barely divides." – B. Goddard Oct 07 '16 at 13:54
Some related older posts: What does $p^\alpha| n$ mean?, Let $p^k$ be the $p$-component of $a^t - 1$ i.e. $p^k|a^t - 1$. Maybe also Notation for "the highest power of $p$ that divides $n$". – Martin Sleziak Oct 08 '16 at 06:59
Even better to follow the existing convention and also explaining the convention! – Oct 08 '16 at 07:08
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p.s. I usually hear this described as "exactly divides". Although I also think I mainly see it when $a$ is prime. – Oct 08 '16 at 07:09
@Hurkyl Well, the concept only makes sense for primes – for example, $4^1 = 2^2$, but $4^2 \nmid 8$ and $2^3 \mid 8$. – Eike Schulte Oct 08 '16 at 21:04

Absolute division symbol?

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