MathDB
no of functions f (max {x + y + 2, xy} ) = min {f (x + y), f (xy + 2)}

Source: 2011 Swedish Mathematical Competition p6

April 30, 2021
algebrafunctionalfunctional equation

Problem Statement

How many functions f:N→Nf:\mathbb N \to \mathbb N are there such that f(0)=2011f(0)=2011, f(1)=111f(1) = 111, and f(max⁡{x+y+2,xy})=min⁡{f(x+y),f(xy+2)}f\left(\max \{x + y + 2, xy\}\right) = \min \{f (x + y), f (xy + 2)\} for all non-negative integers xx, yy?
Back to ProblemsView on AoPS