MathDB

Functional equation

Source: Canada 1969, P8 and Puerto Rico TST 2012, P7

May 14, 2006

functioninductionstrong inductionalgebra unsolvedalgebra

Problem Statement

Let

f

be a function with the following properties:
1)

f(n)

is defined for every positive integer

n

; 2)

f(n)

is an integer; 3)

f(2)=2

; 4)

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

for all

m

and

n

; 5)

f(m)>f(n)

whenever

m>n

.
Prove that

f(n)=n