$32 \cdot 59$ In a right triangle, the lengths of the three sides are integers and form an arithmetic sequence. Then the length of one side could be
(A) 22.
(B) 58.
(C) 81.
(D) 91.
(E) 361.
(32nd American High School Mathematics Examination, 1981)
［Solution］Let the three sides of this right-angled triangle be $s-d, s, s+d$. By the Pythagorean theorem, $(s-d)^{2}+s^{2}=(s+d)^{2}$,

which means
$$
s(s-4 d)=0 \text {. }
$$

Since $s \neq 0$, we have $s-4 d=0$. Thus, $s=4 d$.
Therefore, the lengths of its three sides are $3 d, 4 d, 5 d$, meaning these side lengths must be divisible by 3, 4, or 5.
The only one that meets the above requirement is 81 (divisible by 3).
Therefore, the answer is $(C)$.