Question 176
Prove that $2015 \in M$ and $2016 \notin M$, where
$$
M = \{ x_1 + 2x_2 + 3x_3 + \dots + 2015x_{2015} \mid x_1, x_2, \dots, x_{2015} \in \{-2, 3\} \}.
$$
$$
M = \{ x_1 + 2x_2 + 3x_3 + \dots + 2015x_{2015} \mid x_1, x_2, \dots, x_{2015} \in \{-2, 3\} \}.
$$