3. The polynomial with integer coefficients $P(x)$ satisfies $P(19)=P(94)=1994$, find the constant term of $P(x)$ (it is known that its absolute value is less than 1000).
3. Let the constant term of $P(x)$ be $a_{0}$, then $P(x)=x \cdot Q(x)+a_{0}$, where $Q(x)$ is a polynomial with integer coefficients.
From (1), we get $P(19)=19 n+a_{0}, P(94)=94 m+a_{0}$,

where $n, m$ are integers.
Given $P(19)=P(94)$, we have $19 n=94 m$. Therefore, $m=19 k, n=94 k$, where $k$ is an integer. Then $19 \times 94 k+a_{0}=1994$, which gives $a_{0}=1994-1786 k$. Since $\left|a_{0}\right|<1000$, we get $\quad k=1, a_{0}=208$.
It is worth noting that: such a polynomial can be taken as $P(x)=-(x-19)(x-94)+1994$.