Raportul a doua polinoame pentru o infinitate de n-uri

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Cezar Lupu
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Raportul a doua polinoame pentru o infinitate de n-uri

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Fie \( P, Q\in \mathbb{R}[X] \) si \( \alpha>0 \) astfel incat sa avem

\( \frac{P(n)}{Q(n)}=1^{\alpha}+2^{\alpha}+\ldots + n^{\alpha} \) pentru o infinitate de numere naturale \( n \). Sa se arate ca \( \alpha\in\mathbb{N} \).

Marius Cavachi, R.M.I. C-ta, 2005
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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