MathDB
2013 ToT Fall Senior O p5 f(f(x))=x, g(g(x))=x, f(g(x))>x, g(f(x))>x

Source:

March 22, 2020
functionalgebrainequalities

Problem Statement

Do there exist two integer-valued functions ff and gg such that for every integer xx we have (a) f(f(x))=x,g(g(x))=x,f(g(x))>x,g(f(x))>xf(f(x)) = x, g(g(x)) = x, f(g(x)) > x, g(f(x)) > x ? (b) f(f(x))<x,g(g(x))<x,f(g(x))>x,g(f(x))>xf(f(x)) < x, g(g(x)) < x, f(g(x)) > x, g(f(x)) > x ?