$29 \cdot 32$ Given an integer-coefficient polynomial, a student obtained the results $f(-2) = -56, f(1) = -2, f(3) = 53, f(6) = 528$. Then the one he calculated incorrectly is
(A) $f(-2)$.
(B) $f(1)$.
(C) $f(3)$.
(D) $f(6)$.
(Anhui Province Wuhu City Mathematics Competition, 1993)
[Solution] Let the polynomial with integer coefficients be $p(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{1} x+$ $a_{0}$. Clearly, we have $(m-t) \mid [p(m)-p(t)]$, where $m$ and $t$ are integers.
From this conclusion, we can verify one by one that $f(3)=53$ is incorrect.
Also, $[1-(-2)] \mid [-2-(-56)]$,

but $(3-1) \times [53-(-2)], (3-(-2)) \times (53-(-56))$,
thus the answer is $(C)$.