I recently read here that an odd perfect number, if one exists, would have to be in the form $ p = 36k+9$ or $p = 12k+1$. The link says it was proven In 1953 by Touchard, but I can't seem to find the original or any other proof of this theorem. Does anybody know where I might see the proof of this?
2026-03-27 02:07:09.1774577229
Proof that an odd perfect number must be in the form $ 36k+9$ or $12k+1$
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A very simple explanation can be found at Gazette of Australian mathem. society of Sep 2008 where you can find an article of T.Roberts