13.23 Given the equation $(x-19)(x-83)=p$ has real roots $r_{1}$ and $r_{2}$ (where $p$ is a real number), then the smallest real root of the equation $\left(x-r_{1}\right)\left(x-r_{2}\right)=-p$ is
(A) -19.
(B) -83.
(C) 19.
(D) 83.
(E) 1.
(China Beijing High School Mathematics Competition, 1984; Northeast Three Provinces Mathematics Invitational Competition, 1989)
[Solution] From the given, we have $(x-19)(x-83)-p=\left(x-r_{1}\right)\left(x-r_{2}\right)$,
which means
$$
\left(x-r_{1}\right)\left(x-r_{2}\right)+p=(x-19)(x-83) .
$$

It is easy to see that 19 and 83 are the only two roots of $\left(x-r_{1}\right)\left(x-r_{2}\right)=-p$.
Therefore, the answer is $(C)$.