WakeUp wrote: Let $S$ be a set of integers containing the numbers $0$ and $1996$. Suppose further that any integer root of any non-zero polynomial with coefficients in $S$ also belongs to $S$. Prove that $-2$ belongs to $S$. $-1$ is root of $1996x+1996=0$ and so $-1\in S$ $2$ is root of $-x^{10}-x^9-x^8-x^7-x^6-x^3-x^2+1996=0$ and so $2\in S$ $1$ is root of $-x^2+2x-1=0$ and so $1\in S$ $-2$ is root of $x+2=0$ and so $-2\in S$ Q.E.D.