MathNet 2023-part-06 — 191 problems (EN–VI) Question 63

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