MathDB

2

Part of 2017 International Zhautykov Olympiad

Problems(2)

Sum of distinct prime divisors

Source: IZHO 2017 day p5

1/15/2017
For each positive integer kk denote C(k)C(k) to be sum of its distinct prime divisors. For example C(1)=0,C(2)=2,C(45)=8C(1)=0,C(2)=2,C(45)=8. Find all positive integers nn for which C(2n+1)=C(n)C(2^n+1)=C(n).
number theoryprimesDivisors
IZHO 2017 Functional equations

Source: IZHO 2017 Day 1 Problem 2

1/14/2017
Find all functions f:R→Rf:R \rightarrow R such that (x+y2)f(yf(x))=xyf(y2+f(x))(x+y^2)f(yf(x))=xyf(y^2+f(x)), where x,y∈Rx,y \in \mathbb{R}
functional equationfunctionalgebra