Gradul extinderii divide n!
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Cezar Lupu
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Gradul extinderii divide n!
Fie \( f\in K[X] \) un polinom de grad \( n \) si \( L \) este corpul sau de descompunere peste \( K \). Sa se arate ca \( [L:K] \) divide \( n! \).
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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Tiberiu Popa
- Euclid
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Asta in principiu zice ca daca \( n = \sum_{k=1}^m a_k \), atunci \( \prod_{k=1}^m a_k \) divide \( n! \), care iese usor prin inductie dupa \( m \) (intre \( a_1 + \ldots + a_{m-1} + 1 \) si \( a_1 + \ldots + a_{m-1} + a_m \) avem cel putin un element divizibil cu \( a_m \) - sper sa nu gresesc).
O intrebare: Iese folosind \( S_n \) in vreun fel? La asta ma duce cu gandul \( n! \)...
O intrebare: Iese folosind \( S_n \) in vreun fel? La asta ma duce cu gandul \( n! \)...