Calculate the remainder of the Euclidean division of $2022^{2023^{2024}}$ by 19.
On a $2022 \equiv 8[19]$.

Moreover, we observe that $8^{6} \equiv 1[19]$.

With $q$ and $r$ such that $2023^{2024}=6 q+r$ we therefore have

$$
\begin{aligned}
2022^{2023^{2024}} & \equiv 8^{2023^{2024}} \\
& \equiv 8^{q 6} 8^{r} \\
& \equiv 8^{r}
\end{aligned}
$$

it is therefore sufficient to determine the remainder of the Euclidean division of $2023^{2024}$ by 6.

We proceed in the same way. Since $2023 \equiv 1[6]$ we have $2023^{2024} \equiv 1[6]$ and thus we conclude that

$$
2022^{2023^{2024}} \equiv 8^{1}[19]
$$

which means that the remainder of the Euclidean division is 8 (since $0 \leqslant 8 \leqslant 18$).