It can be shown that for any positive integer $$n$$, the infinitely nested radical expression $\sqrt{ n + \sqrt{n + \sqrt{n + \cdots}}}$ equals a finite number. What is the largest positive integer $$n \le 999$$ such that this expression is equal to a positive integer?

 Details and assumptions:

• A nested radical expression is one which contains a radical inside another, as in $$\sqrt{ 3 + \sqrt{5}}.$$
• An infinitely nested radical expression is one in which the radicals continue to an infinite extent.
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