Cel putin 2^(n/2) inegalitati sunt adevarate

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Filip Chindea
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Cel putin 2^(n/2) inegalitati sunt adevarate

Post by Filip Chindea »

Fie \( n \) un numar intreg pozitiv par. Sa se arate ca exista cel putin \( 2^{n/2} \) alegeri ale semnelor \( \pm \) astfel incat

\( \pm \ x^n \ \pm \ \cdots \ \pm \ x \ < \ 1/2 \)

are loc oricare ar fi \( x \) real.

[ Teste tip OIM 2008 - Problema 1/Test 4 ]
Life is complex: it has real and imaginary components.
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