Conditions Equivalent to the Descartes-Frenicle-Sorli Conjecture on Odd   Perfect Numbers
  The Descartes-Frenicle-Sorli conjecture predicts that $k=1$ if $q^k n^2$ is an odd perfect number with Euler prime $q$. In this note, we present some conditions equivalent to this conjecture. 
Jose Arnaldo B. Dris
math.NT