I got $$P(x)=1+\prod_{i=0}^{2021} (x-i)$$ and need to use Eisensteins's Criteria to solve the irreducibility of $P(x)$ but I found a problem how to elaborate the coefficient and choosing prime $p$. Anyone can help?
2026-04-14 14:55:01.1776178501
How to expand $x(x-1)(x-2)...(x-k)$
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The usual exercise is to show that $$ P(x)=1+\Pi_{i=0}^{2022} (x-i)^2 $$ is irreducible over $\Bbb Q$. This has been solved here:
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$