Question 167
Let $n$ be a positive integer and consider the integers $x_1, x_2, \dots, x_n$, $y_1, y_2, \dots, y_n$ such that
a) $x_1 + x_2 + \dots + x_n = y_1 + y_2 + \dots + y_n = 0$;
b) $x_1^2 + y_1^2 = x_2^2 + y_2^2 = \dots = x_n^2 + y_n^2 = 0$.
Prove that $n$ is an even number.
a) $x_1 + x_2 + \dots + x_n = y_1 + y_2 + \dots + y_n = 0$;
b) $x_1^2 + y_1^2 = x_2^2 + y_2^2 = \dots = x_n^2 + y_n^2 = 0$.
Prove that $n$ is an even number.