Divisibility condition on Sylow numbers

This article gives the statement, and possibly proof, of a constraint on numerical invariants that can be associated with a finite group

This article states a result of the form that one natural number divides another. Specifically, the (number) of a/an/the (Sylow subgroup) divides the (index) of a/an/the (Sylow subgroup).
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Statement

Suppose $G$ is a finite group of order:

$N = p^{k} m$

where $p$ is prime, $k$ is a nonnegative integer, and $m$ is relatively prime to $p$ . Let $n_{p}$ denote the $p$ -Sylow number (?), i.e., the number of $p$ -Sylow subgroups of $G$ . Then we have:

$n_{p} | m$ .

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