MathDB

5

Part of 2005 Chile National Olympiad

Problems(1)

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

10/3/2022
Compute g(2005)g(2005) where gg is a function defined on the natural numbers that has the following properties: i) g(1)=0g(1) = 0 ii) g(nm)=g(n)+g(m)+g(n)g(m)g(nm) = g(n) + g(m) + g(n)g(m) for any pair of integers n,mn, m. iii) g(n2+1)=(g(n)+1)2g(n^2 + 1) = (g(n) + 1)^2 for every integer nn.
number theoryfunctional