MathDB
Weird function

Source: Thailand TSTST 2021, test 2, P3

August 16, 2022
functionalgebra

Problem Statement

Let SS be the set of the positive integers greater than 11, and let nn be from SS. Does there exist a function ff from SS to itself such that for all pairwise distinct positive integers a1,a2,...,ana_1, a_2,...,a_n from SS, we have f(a1)f(a2)...f(an)=f(a1na2n...ann)f(a_1)f(a_2)...f(a_n)=f(a_1^na_2^n...a_n^n)?
Back to ProblemsView on AoPS