MathNet 2010 — Part 03 Question 120

Find all polynomials $P(x, y)$ with real coefficients such that for every $a, b, c \in \mathbb{R}$,
$$
P(ab, c^2 + 1) + P(bc, a^2 + 1) + P(ca, b^2 + 1) = 0
$$