MathDB

8

Part of 1969 Canada National Olympiad

Problems(1)

Functional equation

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

5/14/2006
Let ff be a function with the following properties:
1) f(n)f(n) is defined for every positive integer nn; 2) f(n)f(n) is an integer; 3) f(2)=2f(2)=2; 4) f(mn)=f(m)f(n)f(mn)=f(m)f(n) for all mm and nn; 5) f(m)>f(n)f(m)>f(n) whenever m>nm>n.
Prove that f(n)=nf(n)=n.
functioninductionstrong inductionalgebra unsolvedalgebra