MathDB

function

Source: Ireland 1999

July 4, 2009

functionnumber theoryprime numbersalgebra proposedalgebra

Problem Statement

A function

f: \mathbb{N} \rightarrow \mathbb{N}

satisfies:

(a)

f(ab)\equal{}f(a)f(b) whenever

a

and

b

are coprime;

(b)

f(p\plus{}q)\equal{}f(p)\plus{}f(q) for all prime numbers

p

and

q

. Prove that f(2)\equal{}2,f(3)\equal{}3 and f(1999)\equal{}1999.