MathDB
max X_1^{X_2^{...^{X_k}}} for n = X_1X_2...X_k

Source: 2021 3nd Final Mathematical Cup Senior Division P3 FMC

October 30, 2022
algebranumber theory

Problem Statement

For a positive integer nn we define f(n)=max⁡X1X2...Xkf (n) = \max X_1^{X_2^{...^{X_k}}} where the maximum is taken over all possible decompositions of natural numbers n=X1X2...Xkn = X_1X_2...X_k. Determine f(n)f(n).
Back to ProblemsView on AoPS