Question 1
Let $m,n,p,r$ be integers such that the equations
$$mx^3+nx^2+px+r=2021,$$
$$mx^3+nx^2+px+r=2022,$$
$$mx^3+nx^2+px+r=2023$$
have integer roots $a,b,c$, respectively. Prove that any other roots of these equations are not integers.
$$mx^3+nx^2+px+r=2021,$$
$$mx^3+nx^2+px+r=2022,$$
$$mx^3+nx^2+px+r=2023$$
have integer roots $a,b,c$, respectively. Prove that any other roots of these equations are not integers.