There are given certain positive integer numbers $\displaystyle m,n,d$. Prove that if numbers $\displaystyle m^2n + 1$ and $\displaystyle mn^2 + 1$ are divisible by $\displaystyle d$, then numbers $\displaystyle m^3 + 1$ and $\displaystyle n^3 + 1$ are also divisible by $\displaystyle d$.