Question 38
For arbitrary integer $a, b, c$, we define a function $f(x) = a x^2 + b x + c$. Prove that the expression
$$
f(2020) + f(2019) + \dots + f(1011) - f(1010) - f(1009) - \dots - f(1)
$$
is divisible by $2020$.
$$
f(2020) + f(2019) + \dots + f(1011) - f(1010) - f(1009) - \dots - f(1)
$$
is divisible by $2020$.