# 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.