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Omni-MATH / A positive integer is called [i]downhill[/i] if the digits in its decimal…

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problem

A positive integer is called [i]downhill[/i] if the digits in its decimal representation form a nonstrictly decreasing sequence from left to right. Suppose that a polynomial P(x)P(x) with rational coefficients takes on an integer value for each downhill positive integer xx. Is it necessarily true that P(x)P(x) takes on an integer value for each integer xx?
Plain-text mathematical notation (without MathML)
A positive integer is called [i]downhill[/i] if the digits in its decimal representation form a nonstrictly decreasing sequence from left to right. Suppose that a polynomial P(x) with rational coefficients takes on an integer value for each downhill positive integer x. Is it necessarily true that P(x) takes on an integer value for each integer x?
Original LaTeX notation
A positive integer is called [i]downhill[/i] if the digits in its decimal representation form a nonstrictly decreasing sequence from left to right. Suppose that a polynomial $P(x)$ with rational coefficients takes on an integer value for each downhill positive integer $x$. Is it necessarily true that $P(x)$ takes on an integer value for each integer $x$?

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Source and history

task_id
a86f483b-5a74-578d-918f-c852b6be8a46
task_key
test--a86f483b-5a74-578d-918f-c852b6be8a46
task_revision_id
1
config / split
/ test

Official source

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