vector intreg perpendicular de norma_{infinit} marginita

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Dragos Fratila
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Joined: Thu Oct 04, 2007 10:04 pm

vector intreg perpendicular de norma_{infinit} marginita

Post by Dragos Fratila »

Fie \( a_1<a_2<a_3 \) intregi pozitivi.
Sa se dem ca exista numerele intregi \( x_1,x_2,x_3 \) nu toate nule astfel incat \( a_1x_1+a_2x_2+a_3x_3=0 \) si \( \max_{i=1,2,3}|x_i|\le\frac 2{\sqrt{3}}\sqrt{a_3}+1 \).
Demonstrati si ca \( \frac2{\sqrt3} \) nu poate fi imbunatatit(a).

Miklos Schweitzer 2000
"Greu la deal cu boii mici..."
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