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O problema de Marius Cavachi

 
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andy crisan
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Joined: 28 Dec 2008
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PostPosted: Thu Apr 15, 2010 6:10 pm    Post subject: O problema de Marius Cavachi Reply with quote

Fie A\in\mathcal{M}_{n}(\mathbb{Z}) o matrice inversabila astfel incat pentru orice k\in\mathbb{N} ecuatia X^k=A are solutii in \mathcal{M}_{n}(\mathbb{Z}). Aratati ca  A este matricea unitate.


Marius Cavachi
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turcas
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Joined: 28 Sep 2007
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Location: Simleu Silvaniei, jud Salaj

PostPosted: Sat Apr 17, 2010 3:24 am    Post subject: Reply with quote

Singura solutie pe care o stiu la problema asta, foloseste cunostinte minime de grupuri (si anume, un caz particular al teoremei lui Lagrange). Cred ca daca cititi putin despre grupuri, o sa fie usor de inteles.

Solutia o puteti gasi aici:

http://www.mathlinks.ro/viewtopic.php?search_id=734210645&t=268292

in postul userului NoName.
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