  Dris conjectured in his masters thesis that the inequality $q^k < n$ always
holds, if $N = {q^k}{n^2}$ is an odd perfect number with special prime $q$. In
this note, we initially show that either of the two conditions $n < q^k$ or
$\sigma(q)/n < \sigma(n)/q$ holds. This is achieved by first proving that
$\sigma(q)/n \neq \sigma(n)/q^k$, where $\sigma(x)$ is the sum of the divisors
of $x$. Using this analysis, we further show that the condition $q < n < q^k$
holds in four out of a total of six cases. Finally, we prove that $n < q^k$,
and that this holds unconditionally. This finding disproves both the Dris
Conjecture and the Descartes-Frenicle-Sorli Conjecture that $k = 1$.
