Question 5
Consider a polynomial $P(x,y,z)$ in three variables with integer coefficients such that for any real numbers $a,b,c$, $$P(a,b,c)=0\quad\Longleftrightarrow\quad a=b=c.$$ Find the largest integer $r$ such that for all such polynomials $P(x,y,z)$ and integers $n,m$, $$m^r\mid P(n,n+m,n+2 m).$$