Question 50
Numbers $x_1, x_2, \ldots, x_{2015}$ fulfill both equalities simultaneously:
$x_1^{2014} + x_2^{2014} + \ldots + x_{2015}^{2014} = 1$ and $x_1^{2015} + x_2^{2015} + \ldots + x_{2015}^{2015} = -1$.
$x_1^{2014} + x_2^{2014} + \ldots + x_{2015}^{2014} = 1$ and $x_1^{2015} + x_2^{2015} + \ldots + x_{2015}^{2015} = -1$.