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f(n+1) >= f(n)

Source: China Team Selection Test 2003, Day 2, Problem 1

October 13, 2005

functioninductionlogarithmsalgebra unsolvedalgebra

Problem Statement

Find all functions

f: \mathbb{Z}^+\to \mathbb{R}

, which satisfies

f(n+1)\geq f(n)

for all

n\geq 1

and

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

for all

(m,n)=1