MathDB

g(nm) = g(n) + g(m) + g(n)g(m), g(n^2 + 1) = (g(n) + 1)^2, g(1) = 0

Source: Chile Finals 2005 L2 p5

October 3, 2022

number theoryfunctional

Problem Statement

Compute

g(2005)

where

g

is a function defined on the natural numbers that has the following properties: i)

g(1) = 0

ii)

g(nm) = g(n) + g(m) + g(n)g(m)

for any pair of integers

n, m

. iii)

g(n^2 + 1) = (g(n) + 1)^2

for every integer

n