Numerele Fermat nu pot fi perfecte

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Cezar Lupu
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Numerele Fermat nu pot fi perfecte

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Sa se arate ca numerele Fermat \( F_{n}=2^{2^{n}}+1 \) nu pot face parte dintr-o pereche amiabila si nu pot fi nici perfecte.

[Florian Luca, American Mathematical Monthly, 2000]
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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