4

Part of 2009 Ukraine Team Selection Test

Problems(1)

f(x^{n+1}+(y^{n+1})=x^n f(x)+y^n f(y) when x,y>0

Source: Ukraine TST 2009 p4

n

be some positive integer. Find all functions

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

(i.e., functions defined by the set of all positive real numbers with real values) for which equality holds

f\left( {{x}^{n+1}}+ {{y}^{n+1}} \right)={{x}^{n}}f\left( x \right)+{{y}^{n}}f\left( y \right)

for any positive real numbers

x, y

functional equationfunctionalalgebra