Question 171
Let $p$ be a prime number. Determine the maximal degree of a polynomial $T(x)$ whose coefficients belong to $\{0,1,...,p-1\}$ whose degree is less than $p$, and which satisfies
$$
T(n) \equiv T(m) \pmod{p} \implies n \equiv m \pmod{p}
$$
for all integers $n, m$.
$$
T(n) \equiv T(m) \pmod{p} \implies n \equiv m \pmod{p}
$$
for all integers $n, m$.