TR-MO 2000 Problem 4

Let $p$ be a prime number. $T(x)$ is a polynomial with integer coefficients and degree from the set $\{0,1,...,p-1\}$ and such that $T(n) \equiv T(m) (mod p)$ for some integers m and n implies that $m \equiv n (mod p)$ . Determine the maximum possible value of degree of $T(x)$