olymmath

USAMO 2019 Problem 6

  • Day 2

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

Dataset text AI-MO AoPS. Quoted with source.

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