Question 95
Let $a_1, \dots, a_{2016}$ and $b_1, \dots, b_{2016}$ be two reorderings of the numbers $1, \dots, 2016$. Prove that
$$
2017 \mid a_i b_i - a_j b_j
$$
for some distinct indices $i$ and $j$.
$$
2017 \mid a_i b_i - a_j b_j
$$
for some distinct indices $i$ and $j$.