VTMO 2026 - Grade 8 - Semifinal - SET 06 - Self-study Question 16

Integers $m,n,p,r$ are such that the equations $mx^3+nx^2+px+r=2021$, $mx^3+nx^2+px+r=2022$, and $mx^3+nx^2+px+r=2023$ have integer roots $a,b,c$, respectively. Prove $a+c=2b$.