9.3. Will the equation $x^{2019}+2 x^{2018}+3 x^{2017}+\cdots+2019 x+2020=0$ have integer roots
Answer: No.

Solution. If there is an integer root $a$, then $ab^{2019}, 4 b^{2016}>3 b^{2017}, \ldots, 2020>2019 b$.

If $b \geq 2$, then $b^{2019} \geq 2 b^{2018}, 3 b^{2017}>4 b^{2016}, \ldots, 2019 b>2020$.

Therefore, there are no integer roots.