2023 SSMO Relay Round 1 Problems/Problem 1

Problem

Compute the remainder when $2022^{2021^{2020^{\dots}}}$ is divided by $2023$.

Solution

Notice that over mod $2023$, we have $2022^{2021^{2020^{\dots}}}\equiv(-1)^{2021^{2020^{\dots}}}$. Since the power is odd, we conclude that the remainder must be $-1\equiv\boxed{2022}$.

~ eevee9406