$32 \cdot 63$ In a right triangle, the hypotenuse $c$ and one leg $a$ are consecutive integers, then the square of the other leg is
(A) $c a$.
(B) $\frac{c}{a}$.
(C) $c+a$.
(D) $c=a$.
(E) None of the above.
(7th American High School Mathematics Examination, 1956)
[Solution] Let $a=n, c=n+1$, then we have
$$
(n+1)^{2}-n^{2}=2 n+1=(n+1)+n=a+c \text {. }
$$

Therefore, the answer is (C).