Question 109
Consider a polynomial $P(x, y, z)$ in three variables with integer coefficients such that for any real numbers $a, b, c$,
$$
P(a, b, c) = 0 \Leftrightarrow a = b = c.
$$
Find the largest integer $r$ such that for all such polynomials $P(x, y, z)$ and integers $n, m$,
$$
m^r \mid P(n, n+m, n+2m).
$$
$$
P(a, b, c) = 0 \Leftrightarrow a = b = c.
$$
Find the largest integer $r$ such that for all such polynomials $P(x, y, z)$ and integers $n, m$,
$$
m^r \mid P(n, n+m, n+2m).
$$