$33 \cdot 30$ Let $m$ be a given natural number, the number of integers $a$ that satisfy $[a-\sqrt{a}]=m$ is (where $[x]$ denotes the greatest integer not exceeding $x$)
(A) Exactly one.
(B) Exactly two.
(C) No less than two.
(D) No more than two.
(China Jiangxi Province Nanchang City Junior High School Mathematics Competition, 1991)
[Solution 1] From the given $[a-\sqrt{a}]=m$,
let $m=1$, it can be deduced that $a=3$.
let $m=2$, it can be deduced that $a=4,5$.
Thus, we can eliminate $(A),(B),(C)$.
Therefore, the answer is $(D)$.
[Solution 2] If $a$ is a perfect square, then there is only one $a$ that satisfies $[a-\sqrt{a}]=m$. Otherwise, let $a-\sqrt{a}=m+r$, where $0 \leqslant r < 1$, then $\Delta>0$, which can eliminate $(A)$. Therefore, the answer is $(D)$.