MathDB

6

Part of 2019 USAMO

Problems(1)

Sad Algebra

Source: 2019 USAMO 6, by Titu Andreescu and Gabriel Dospinescu

4/18/2019
Find all polynomials PP with real coefficients such that P(x)yz+P(y)zx+P(z)xy=P(x−y)+P(y−z)+P(z−x)\frac{P(x)}{yz}+\frac{P(y)}{zx}+\frac{P(z)}{xy}=P(x-y)+P(y-z)+P(z-x) holds for all nonzero real numbers x,y,zx,y,z satisfying 2xyz=x+y+z2xyz=x+y+z.
Proposed by Titu Andreescu and Gabriel Dospinescu
USAMOsad storiessadder2019 USAMO Problem 6PolynomialsWeird problemthe saddest