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Omni-MATH / Find all pairs of integers a,b for which there exists a polynomial P(x)∈Z[X] such that product (x²+ax+b)⋅P(x) is a polynomial of a form x^(n)+c_(n−1)x^(n−1)+⋯+c₁x+c₀ where each of …

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problem

Find all pairs of integers a,ba,b for which there exists a polynomial P(x)∈Z[X]P(x) \in \mathbb{Z}[X] such that product (x2+ax+b)⋅P(x)(x^2+ax+b)\cdot P(x) is a polynomial of a form xn+cn−1xn−1+⋯+c1x+c0 x^n+c_{n-1}x^{n-1}+\cdots+c_1x+c_0 where each of c0,c1,…,cn−1c_0,c_1,\ldots,c_{n-1} is equal to 11 or −1-1.
Plain-text mathematical notation (without MathML)
Find all pairs of integers a,b for which there exists a polynomial P(x)∈Z[X] such that product (x²+ax+b)⋅P(x) is a polynomial of a form x^(n)+c_(n−1)x^(n−1)+⋯+c₁x+c₀ where each of c₀,c₁,…,c_(n−1) is equal to 1 or −1.
Original LaTeX notation
Find all pairs of integers $a,b$ for which there exists a polynomial $P(x) \in \mathbb{Z}[X]$ such that product $(x^2+ax+b)\cdot P(x)$ is a polynomial of a form \[ x^n+c_{n-1}x^{n-1}+\cdots+c_1x+c_0  \] where each of $c_0,c_1,\ldots,c_{n-1}$ is equal to $1$ or $-1$.

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Source and history

task_id
dfd99724-7e1a-5cbe-a3ac-0b9aa04faa89
task_key
test--dfd99724-7e1a-5cbe-a3ac-0b9aa04faa89
task_revision_id
1
config / split
/ test

Official source

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