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Gasiti numerele!

 
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Marius Mainea
Gauss


Joined: 26 May 2008
Posts: 1099
Location: Gaesti (Dambovita)

PostPosted: Sun Jan 25, 2009 10:13 pm    Post subject: Gasiti numerele! Reply with quote

Sunt patru numere intregi pozitive. Daca s-ar cunoaste produsul lor s-ar sti si numerele.La fel, daca s-ar cunoaste suma patratelor lor. Dar daca s-ar cunoste suma numerelor, acestea nu s-ar putea deduce.

Care sunt cele patru numere?

Concursul ,,Cezar Ivanescu'', 2009


Last edited by Marius Mainea on Sun Jan 25, 2009 11:44 pm; edited 1 time in total
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Beniamin Bogosel
Co-admin


Joined: 07 Mar 2008
Posts: 760
Location: Chambery, Franta

PostPosted: Sun Jan 25, 2009 11:28 pm    Post subject: Reply with quote

mi se pare ca se contrazic ipotezele...
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seby97
Euclid


Joined: 04 Aug 2011
Posts: 31

PostPosted: Tue Jan 10, 2012 1:03 am    Post subject: Reply with quote

Un exemplu ar putea fi 1,1,1,3.Atunci produsul ar fi 3 si s-ar deduce usor care sunt numerele,iar suma patratelor lor este 12(am considerat ca un numar intreg pozitiv este diferit de 0).Totusi suma lor este 6 din care nu se pot deduce exact numerele(exista 2 cazuri).Acum nu stiu daca problema se refera la faptul ca numerele se pot deduce cu exactitate sau pot exista cazuri(cum e si cazul "rezultatului" gasit de mine)
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