I Don't Think the a Should be There

Calculus Level 5

x=1log33((x+a1)(x+a+1)(x+a3)(x+a+3))=1\displaystyle \sum_{x=1}^{\infty} \displaystyle \log_{33}\left(\frac{(x+a-1)(x+a+1)}{(x+a-3)(x+a+3)}\right)=1

If the sum of all possible real values of constant aa such that the infinite sum above is fulfilled can be represented as pq\frac{p}{q} for coprime positive integers p,qp,q, find p+qp+q.

Try the harder (way harder) version here.

Try the easier version here.


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