Problem

Source: Swiss TST 2023 P7

Tags: algebra



Find all monic polynomials $P(x)=x^{2023}+a_{2022}x^{2022}+\ldots+a_1x+a_0$ with real coefficients such that $a_{2022}=0$, $P(1)=1$ and all roots of $P$ are real and less than $1$.