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Omni-MATH / Given distinct prime numbers p and q and a natural number n≥3, find all a∈Z such that the polynomial f(x)=x^(n)+ax^(n−1)+pq can be factored into 2 integral polynomials of degree at…

Problem

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problem

Given distinct prime numbers

p

and

q

and a natural number

n \geq 3

, find all

a \in \mathbb{Z}

such that the polynomial

f(x) = x^n + ax^{n-1} + pq

can be factored into 2 integral polynomials of degree at least 1.

Plain-text mathematical notation (without MathML)

Given distinct prime numbers p and q and a natural number n≥3, find all a∈Z such that the polynomial f(x)=x^(n)+ax^(n−1)+pq can be factored into 2 integral polynomials of degree at least 1.

Original LaTeX notation

Given distinct prime numbers $p$ and $q$ and a natural number $n \geq 3$, find all $a \in \mathbb{Z}$ such that the polynomial $f(x) = x^n + ax^{n-1} + pq$ can be factored into 2 integral polynomials of degree at least 1.

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task_id: 5bc7f3d6-a55e-52e9-ad57-4cb842456793
task_key: test--5bc7f3d6-a55e-52e9-ad57-4cb842456793
task_revision_id: 3
config / split: / test

Official source

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