# Now there's an $$n$$?

Calculus Level 4

$\large\displaystyle \sum_{x=1}^{\infty} \displaystyle \log_{n}\left(\frac{(x+a-1)(x+a+1)}{(x+a-3)(x+a+3)}\right)=1$

Solve for the maximum positive integral value of $$n$$ such that there is exactly 1 positive rational solution for $$a$$.

Here is an easier version.

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