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Omni-MATH / For a polynomialƒ P and a positive integer n, define P_(n) as the number of positive integer pairs (a,b) such that a<b≤n and |P(a)|−|P(b)| is divisible by n. Determine all polynomi…

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problem

For a polynomialƒ PP and a positive integer nn, define PnP_{n} as the number of positive integer pairs (a,b)(a, b) such that a<b≤na<b \leq n and |P(a)|−|P(b)||P(a)|-|P(b)| is divisible by nn. Determine all polynomial PP with integer coefficients such that for all positive integers n,Pn≤2021n, P_{n} \leq 2021.
Plain-text mathematical notation (without MathML)
For a polynomialƒ P and a positive integer n, define P_(n) as the number of positive integer pairs (a,b) such that a<b≤n and |P(a)|−|P(b)| is divisible by n. Determine all polynomial P with integer coefficients such that for all positive integers n,P_(n)≤2021.
Original LaTeX notation
For a polynomialƒ $P$ and a positive integer $n$, define $P_{n}$ as the number of positive integer pairs $(a, b)$ such that $a<b \leq n$ and $|P(a)|-|P(b)|$ is divisible by $n$. Determine all polynomial $P$ with integer coefficients such that for all positive integers $n, P_{n} \leq 2021$.

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Source and history

task_id
60484837-79cd-5fee-b693-281affdb0e60
task_key
test--60484837-79cd-5fee-b693-281affdb0e60
task_revision_id
1
config / split
/ test

Official source

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