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Omni-MATH / Let Z denote the set of all integers. Find all polynomials P(x) with integer coefficients that satisfy the following property: For any infinite sequence a₁,a₂,… of integers in whic…

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problem

Let Z\mathbb{Z} denote the set of all integers. Find all polynomials P(x)P(x) with integer coefficients that satisfy the following property: For any infinite sequence a1,a2,…a_{1}, a_{2}, \ldots of integers in which each integer in Z\mathbb{Z} appears exactly once, there exist indices i<ji<j and an integer kk such that ai+ai+1+⋯+aj=P(k)a_{i}+a_{i+1}+\cdots+a_{j}=P(k).
Plain-text mathematical notation (without MathML)
Let Z denote the set of all integers. Find all polynomials P(x) with integer coefficients that satisfy the following property: For any infinite sequence a₁,a₂,… of integers in which each integer in Z appears exactly once, there exist indices i<j and an integer k such that a_(i)+a_(i+1)+⋯+a_(j)=P(k).
Original LaTeX notation
Let \(\mathbb{Z}\) denote the set of all integers. Find all polynomials \(P(x)\) with integer coefficients that satisfy the following property: For any infinite sequence \(a_{1}, a_{2}, \ldots\) of integers in which each integer in \(\mathbb{Z}\) appears exactly once, there exist indices \(i<j\) and an integer \(k\) such that \(a_{i}+a_{i+1}+\cdots+a_{j}=P(k)\).

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Source and history

task_id
a7d44f79-0992-5bf3-be5c-ae65958fbff2
task_key
test--a7d44f79-0992-5bf3-be5c-ae65958fbff2
task_revision_id
1
config / split
/ test

Official source

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