MathNet 2022-part-05 — 197 problems (EN–VI) Question 174

Does there exist a trinomial $f(x) = ax^2 + bx + c$ with integer coefficients such that $a$ isn't divisible by $2022$ and all numbers $f(1), f(2), \ldots, f(2022)$ give different remainders under the division by $2022$?