Things get tricky here

Algebra Level pending
• $$n$$ and $$a$$ are different real integers, where $$n≥0$$ and $$a≥0$$. Which of the following equations have the most real pair of integral solutions $$(a,n)$$ for any positive integer $$a$$?

• 1.$$\sqrt n - \sqrt{a-n} = a$$.

• 2.$$\sqrt n - \sqrt{n-a} = a$$
• 3.$$\sqrt n + \sqrt{a-n} = a$$
• 4.$$\sqrt n + \sqrt{n-a} = a$$

• Type your answer (1,2,3,or 4) and try not to use luck to finish this question lol.

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