1. (1996 National High School Competition Question) There exists an integer $n$, such that $\sqrt{p+n}+\sqrt{n}$ is an integer for the prime number $p(\quad)$.
A. Does not exist
B. Only one
C. More than one, but a finite number
D. Infinitely many
1. D. Let $p=2k+1$ be an odd prime, and let $n=k^{2}$, then $\sqrt{p+n}+\sqrt{n}=\sqrt{2k+1+k^{2}}+\sqrt{k^{2}}=2k+1$. Therefore, the answer is D.