Question 145
Each of the numbers $x_{1}, x_{2}, \ldots, x_{2004}$ can be equal to $\sqrt{2}-1$ or $\sqrt{2}+1$. How many distinct integer values can the sum $$
\sum_{k=1}^{1002} x_{2k-1} x_{2k} = x_{1} x_{2} + x_{3} x_{4} + x_{5} x_{6} + \cdots + x_{2003} x_{2004}
$$ assume?
\sum_{k=1}^{1002} x_{2k-1} x_{2k} = x_{1} x_{2} + x_{3} x_{4} + x_{5} x_{6} + \cdots + x_{2003} x_{2004}
$$ assume?