Problem

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E+16

Tags: number theory



What is the remainder of $2025\wedge (2024\wedge (2022\wedge (2021\wedge (2020\wedge ...\wedge (2\wedge 1) . . .)))))$ when it is divided by $2023$? Here $\wedge$ is the exponential symbol, for example $2\wedge (3\wedge 2) = 2\wedge 9 = 512$. The power tower contains the integers from $2025$ to $1$ exactly once, except that the number $2023$ is missing.