Note que
\(\frac{\partial v}{\partial x_1} x_1 + \cdots + \frac{\partial v}{\partial x_n} x_n = \left( \frac{\partial u}{\partial x_1} -\frac{a}{x_1+\cdots+x_n} \right) x_1 + \cdots + \left( \frac{\partial u}{\partial x_n} -\frac{a}{x_1+\cdots+x_n} \right) x_n\)
Logo,
\[ \sum_{i=1}^{n} x_i \frac{\partial v}{\partial x_i} = \sum_{i=1}^{n} x_i \frac{\partial u}{\partial x_i} -a \sum_{i=1}^{n} \frac{x_i}{x_i} = a - a = 0 \]
Logo, usando o teorema de Euler,
\[ \sum_{i=1}^{n} x_i \frac{\partial v}{\partial x_i}=n \nu(x_1,\cdots,x_n),\]
encontramos que \(n=0\).