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Omni-MATH / Find all polynomials P with real coefficients such that (P(x))/(yz)+(P(y))/(zx)+(P(z))/(xy)=P(x−y)+P(y−z)+P(z−x) holds for all nonzero real numbers x,y,z satisfying 2xyz=x+y+z .

Problem

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problem

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 .
Plain-text mathematical notation (without MathML)
Find all polynomials P with real coefficients such that (P(x))/(yz)+(P(y))/(zx)+(P(z))/(xy)=P(x−y)+P(y−z)+P(z−x) holds for all nonzero real numbers x,y,z satisfying 2xyz=x+y+z .
Original LaTeX notation
Find all polynomials $P$ with real coefficients such that \[\frac{P(x)}{yz}+\frac{P(y)}{zx}+\frac{P(z)}{xy}=P(x-y)+P(y-z)+P(z-x)\] holds for all nonzero real numbers $x,y,z$ satisfying $2xyz=x+y+z$ .

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Source and history

task_id
fb339ec3-5ec4-5fa3-b045-7f34a8cce1e1
task_key
test--fb339ec3-5ec4-5fa3-b045-7f34a8cce1e1
task_revision_id
1
config / split
/ test

Official source

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