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Looking for a proof different from the standard proof(s) of a result
2
votes
Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive ...
EDIT 2015.07.15 I believe there is no such integer $x$. See below for the rest of the edit. END EDIT 2015.07.15
I had some initial thoughts which seemed promising. They do not lead to a proof, but …
1
vote
Accepted
Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive ...
I've decided to collect some basic observations and references for the benefit
of future readers.
A more challenging problem is to ask for integers $m$ and $p$ such that for all
integers $k$, $p_0 = …