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Omni-MATH / A polynomial f(x) with real coefficients is called [i]generating[/i], if for each polynomial φ(x) with real coefficients there exists a positive integer k and polynomials …

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problem

A polynomial f(x)f(x) with real coefficients is called [i]generating[/i], if for each polynomial φ(x)\varphi(x) with real coefficients there exists a positive integer kk and polynomials $g_1(x),\dotsc,g_k(x)$ with real coefficients such that \[\varphi(x)=f(g_1(x))+\dotsc+f(g_k(x)).\] Find all generating polynomials.
Plain-text mathematical notation (without MathML)
A polynomial f(x) with real coefficients is called [i]generating[/i], if for each polynomial φ(x) with real coefficients there exists a positive integer k and polynomials $g_1(x),\dotsc,g_k(x)$ with real coefficients such that
\[\varphi(x)=f(g_1(x))+\dotsc+f(g_k(x)).\]
Find all generating polynomials.
Original LaTeX notation
A polynomial $f(x)$ with real coefficients is called [i]generating[/i], if for each polynomial $\varphi(x)$ with real coefficients there exists a positive integer $k$ and polynomials $g_1(x),\dotsc,g_k(x)$ with real coefficients such that
\[\varphi(x)=f(g_1(x))+\dotsc+f(g_k(x)).\]
Find all generating polynomials.

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task_id
49d2368e-56fb-5fc9-a0bc-70015213da24
task_key
test--49d2368e-56fb-5fc9-a0bc-70015213da24
task_revision_id
1
config / split
/ test

Official source

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