Exercise 1.

Let $m = x^3 - 1$ and $n = x^2 + 1$ be polynomials in ${\mbox{${\mathbb{Q}}$}}[x]$ . Find all polynomials $p$ of degree less than 5 satisfying the system of equations

$$\left\{ \begin{array}{l} p \equiv 1 \mod{\, m} \\ p \equiv 2 \mod{\, n} \\ \end{array} \right.$$ (3)