Question 6
Find all real-coefficient polynomials $P$ such that
$$\frac{P(x)}{yz}+\frac{P(y)}{zx}+\frac{P(z)}{xy}=P(x-y)+P(y-z)+P(z-x)$$
for all nonzero real $x,y,z$ satisfying $2xyz=x+y+z$.
Proposed by Titu Andreescu, Gabriel Dospinescu. Source: Evan Chen’s third-party solution notes.
$$\frac{P(x)}{yz}+\frac{P(y)}{zx}+\frac{P(z)}{xy}=P(x-y)+P(y-z)+P(z-x)$$
for all nonzero real $x,y,z$ satisfying $2xyz=x+y+z$.
Proposed by Titu Andreescu, Gabriel Dospinescu. Source: Evan Chen’s third-party solution notes.