MathDB
Function

Source: Junior Olympiad of Malaysia Shortlist 2015 N7

July 17, 2015
functionnumber theory

Problem Statement

Find all functions f:N→N0 f:\mathbb{N} \rightarrow \mathbb{ N }_0 satisfy the following conditions:
i) f(ab)=f(a)+f(b)−f(gcd⁡(a,b)),∀a,b∈N f(ab)=f(a)+f(b)-f(\gcd(a,b)), \forall a,b \in \mathbb{N}
ii) For all primes p p and natural numbers a a , f(a)≥f(ap)⇒f(a)+f(p)≥f(a)f(p)+1 f(a)\ge f(ap) \Rightarrow f(a)+f(p) \ge f(a)f(p)+1
Back to ProblemsView on AoPS