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Omni-MATH / For any positive integer k, denote the sum of digits of k in its decimal representation by S(k). Find all polynomials P(x) with integer coefficients such that for any positive inte…

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problem

For any positive integer kk, denote the sum of digits of kk in its decimal representation by S(k)S(k). Find all polynomials P(x)P(x) with integer coefficients such that for any positive integer n≥2016n \geq 2016, the integer P(n)P(n) is positive and S(P(n))=P(S(n)).S(P(n)) = P(S(n)). [i]
Plain-text mathematical notation (without MathML)
For any positive integer k, denote the sum of digits of k in its decimal representation by S(k). Find all polynomials P(x) with integer coefficients such that for any positive integer n≥2016, the integer P(n) is positive and S(P(n))=P(S(n)).

[i]
Original LaTeX notation
For any positive integer $k$, denote the sum of digits of $k$ in its decimal representation by $S(k)$. Find all polynomials $P(x)$ with integer coefficients such that for any positive integer $n \geq 2016$, the integer $P(n)$ is positive and $$S(P(n)) = P(S(n)).$$

[i]

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Source and history

task_id
5006af5a-19a6-5069-b26f-e607bbb178ec
task_key
test--5006af5a-19a6-5069-b26f-e607bbb178ec
task_revision_id
1
config / split
/ test

Official source

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