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Function number theory

Source: Iran second round 2016,day2,problem6

April 29, 2016
functionnumber theory

Problem Statement

Find all functions f:N→Nf: \mathbb N \to \mathbb N Such that: 1.for all x,y∈Nx,y\in N:x+y∣f(x)+f(y)x+y|f(x)+f(y) 2.for all x≥1395x\geq 1395:x3≥2f(x)x^3\geq 2f(x)
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