Problema 3, lista scurta 2009
Posted: Mon May 25, 2009 9:23 pm
Fie \( x\ ,\ y\ ,\ z\ \in\ \mathbb{C} \). Sa se determine toate numerele naturale (strict) pozitive \( n \) astfel incat
sistemul de ecuatii : \( \left{\ \begin{array}{ccc}
x&+&y&+&z & = & 3& \\\\
x^2&+&y^2&+&z^2 & = & 3 & \\\\
x^n&+&y^n&+&z^n & = & 3 & \end{array} \) are solutia unica \( x=y=z=1 \) .
sistemul de ecuatii : \( \left{\ \begin{array}{ccc}
x&+&y&+&z & = & 3& \\\\
x^2&+&y^2&+&z^2 & = & 3 & \\\\
x^n&+&y^n&+&z^n & = & 3 & \end{array} \) are solutia unica \( x=y=z=1 \) .