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MathNet 2016-part-03 — 184 problems (EN–VI) Question 50

Math Olympiad Vault · MathNet 2016-part-03 — 184 problems (EN–VI)

Question 50

Let $f$ be a real-valued function such that
$$
f(x-f(y))=f(x)-x f(y)
$$
for any real numbers $x$ and $y$. If $f(0)=3$, determine $f(2016)-f(2013)$.