A short proof for the Descartes-Frenicle-Sorli conjecture on odd perfect numbers

If $N=q^k{n}^2$ is an odd perfect number given in Eulerian form, then the Descartes-Frenicle-Sorli conjecture predicts that $k={\nu }_q(N)=1$. In this article, we give a short proof for this conjecture.