MathDB

2014 preRMO p18, f(mn) = f(m)f(n), f 1-1, N-> N, f (999) ?

Source:

August 9, 2019

functionalgebraminimum

Problem Statement

Let

f

be a one-to-one function from the set of natural numbers to itself such that

f(mn) = f(m)f(n)

for all natural numbers

m

and

n

. What is the least possible value of

f (999)