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Omni-MATH / Find, with proof, all nonconstant polynomials P(x) with real coefficients such that, for all nonzero real numbers z with P(z)≠0 and P((1)/(z))≠0, we have …

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problem

Find, with proof, all nonconstant polynomials P(x)P(x) with real coefficients such that, for all nonzero real numbers zz with P(z)≠0P(z) \neq 0 and P(1z)≠0P\left(\frac{1}{z}\right) \neq 0, we have 1P(z)+1P(1z)=z+1z\frac{1}{P(z)}+\frac{1}{P\left(\frac{1}{z}\right)}=z+\frac{1}{z}
Plain-text mathematical notation (without MathML)
Find, with proof, all nonconstant polynomials P(x) with real coefficients such that, for all nonzero real numbers z with P(z)≠0 and P((1)/(z))≠0, we have (1)/(P(z))+(1)/(P((1)/(z)))=z+(1)/(z)
Original LaTeX notation
Find, with proof, all nonconstant polynomials $P(x)$ with real coefficients such that, for all nonzero real numbers $z$ with $P(z) \neq 0$ and $P\left(\frac{1}{z}\right) \neq 0$, we have $$\frac{1}{P(z)}+\frac{1}{P\left(\frac{1}{z}\right)}=z+\frac{1}{z}$$

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task_id
48127047-3c16-55e9-a1d0-d0c1947f869c
task_key
test--48127047-3c16-55e9-a1d0-d0c1947f869c
task_revision_id
1
config / split
/ test

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