Question 109
Find all pairs of polynomials $p(x), q(x) \in \mathbb{R}[x]$ satisfying the equality
$$
p(x^2) = p(x)q(1-x) + p(1-x)q(x)
$$
for all real $x$.
$$
p(x^2) = p(x)q(1-x) + p(1-x)q(x)
$$
for all real $x$.
MathNet 2015-part-01 — 191 problems (EN–VI) Question 109
Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)