MathNet 2022-part-01 — 197 problems (EN–VI) Question 119

Consider a quadratic polynomial $f(x)$ with integer coefficients. If the values $f(0)$, $f(3)$, and $f(4)$ are pairwise different numbers from the set $\{2, 20, 202, 2022\}$, then determine all possible values for $f(1)$.