Shortlist 19
Posted: Sun Mar 28, 2010 8:47 pm
Demonstrati ca daca o functie \( f:{R}\rightarrow{R} \) are proprietatea:
\( |\sum_{k=1}^n 2^k(f(x+ky)-f(x-ky))|\le1 \), oricare \( n\in\mathbb{N}* \) si oricare \( x,y\in\mathbb{R} \), atunci f este constanta.
Farcas Csaba, Cluj, Shortlist 2007
\( |\sum_{k=1}^n 2^k(f(x+ky)-f(x-ky))|\le1 \), oricare \( n\in\mathbb{N}* \) si oricare \( x,y\in\mathbb{R} \), atunci f este constanta.
Farcas Csaba, Cluj, Shortlist 2007