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4

It does not seem useful to me to just repeat the solution in e.g. Ian Stewart's book Another Fine Math You've Got Me Into... as linked from the Wikipedia Moving sofa problem page, so I'll just describe how I understood it. (Note: This is take 2.) Consider the situation when the sofa is rotated 45 degrees with respect to the corner. In order to fit into ...


3

Let $N = {q^k}{n^2}$ be an odd perfect number given in Eulerian form. Let $$I(x) = \dfrac{\sigma(x)}{x}$$ be the abundancy index of $x$. This is a partial answer to the original question, and proves the claim in the affirmative, subject to the validity of a recent proof claim by Patrick A. Brown that $q^k < n$ holds (in many cases). First, we show the ...



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