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Omni-MATH / Let α be a real number. Determine all polynomials P with real coefficients such that P(2x+α)≤(x²⁰+x¹⁹)P(x) holds for all real numbers x.

Problem

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problem

Let α\alpha be a real number. Determine all polynomials PP with real coefficients such that P(2x+α)≤(x20+x19)P(x)P(2x+\alpha)\leq (x^{20}+x^{19})P(x) holds for all real numbers xx.
Plain-text mathematical notation (without MathML)
Let α be a real number. Determine all polynomials P with real coefficients such that P(2x+α)≤(x²⁰+x¹⁹)P(x) holds for all real numbers x.
Original LaTeX notation
Let $\alpha$ be a real number. Determine all polynomials $P$ with real coefficients such that $$P(2x+\alpha)\leq (x^{20}+x^{19})P(x)$$ holds for all real numbers $x$.

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Source and history

task_id
3799c3e3-cc83-5cf3-846e-dcec1aa51328
task_key
test--3799c3e3-cc83-5cf3-846e-dcec1aa51328
task_revision_id
1
config / split
/ test

Official source

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