# exactly divides

Let $a$ and $b$ be integers and $n$ a positive integer.  Then $a^{m}$ exactly divides $b$ (denoted as $a^{n}\parallel n$) if $a^{n}$ divides $b$ but $a^{n+1}$ does not divide $b$.  For example,  $2^{4}\parallel 48$.

One can, of course, use the similar expression and notation for the elements $a$, $b$ of any commutative ring or monoid (cf. e.g. divisor as factor of principal divisor).

Title exactly divides ExactlyDivides 2013-03-22 16:10:44 2013-03-22 16:10:44 Wkbj79 (1863) Wkbj79 (1863) 7 Wkbj79 (1863) Definition msc 11A51 Divides Divisibility DivisibilityInRings