[Sulution] Cute problem with a+b+c = 2022

 The problem was here.

The goal was to minimize manual algebra.

Let $ab + bc  + ac = s$. Then $abc = 2022s$ and thus $a,b,c$ are roots of the polynomial

$$ t^3 - 2022t^2 + st - 2022s = (t-2022)(t^2 + s) $$

Thus we can assume $a = 2022, b = -c$ and thus the answer is $2022^{-2023}$.