Question 37
Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ with the following property:
$$
\text{If } x + y + z = 0, \text{ then } f(x) + f(y) + f(z) = xyz .
$$
$$
\text{If } x + y + z = 0, \text{ then } f(x) + f(y) + f(z) = xyz .
$$
MathNet 2007-part-01 — 187 problems (EN–VI) Question 37
Math Olympiad Vault · MathNet 2007-part-01 — 187 problems (EN–VI)