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f ( x / (y + 1)) = 1 - xf(x + y)

Source: Switzerland - 2013 Swiss MO Final Round p4

December 30, 2022

algebrafunctionalfunctional equation

Problem Statement

Find all functions

f : R_{>0} \to R_{>0}

with the following property:

f \left( \frac{x}{y + 1}\right) = 1 - xf(x + y)

for all

x > y > 0