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JBTST I 2010, Problema 4

 
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Andi Brojbeanu
Newton


Joined: 22 Mar 2009
Posts: 383
Location: Targoviste (Dambovita)

PostPosted: Mon Apr 12, 2010 10:50 pm    Post subject: JBTST I 2010, Problema 4 Reply with quote

Fie n un numar natural neneul si numerele intregi x_1, x_2, ...., x_n, y_1, y_2, ...., y_n cu proprietatile:
a)x_1+x_2+....+x_n=y_1+y_2+....+y_n=0;
b)x_1^2+y_1^2=x_2^2+y_2^2=....=x_n^2+y_n^2.
Sa se arate ca n este par.
Dan Nedeianu
_________________
Brojbeanu Andi Gabriel, clasa XII-a
Colegiul National "Constantin Carabella" Targoviste
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