MathDB
2025^.... mod 2023

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

May 25, 2024
number theory

Problem Statement

What is the remainder of 2025(2024(2022(2021(2020...(21)...)))))2025\wedge (2024\wedge (2022\wedge (2021\wedge (2020\wedge ...\wedge (2\wedge 1) . . .))))) when it is divided by 20232023?
Here \wedge is the exponential symbol, for example 2(32)=29=5122\wedge (3\wedge 2) = 2\wedge 9 = 512. The power tower contains the integers from 20252025 to 11 exactly once, except that the number 20232023 is missing.