Is this product: \begin{align*} \prod_{\text{$p$ prime}}\frac{p^2+1}{p^2-1} \end{align*} rational? What is the value of it? What about for the natural numbers $p>1$?
Is the product $(p^2+1)/(p^2-1)$ for all $p$ rational? For all $n$?
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number-theory
prime-numbers
infinite-product
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1Do you mean $\frac{p^2 + 1}{p^2 - 1}$, rather than $p^2 + p^{-2} - 1$? – 2017-02-19
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0Yes, sorry, your right – 2017-02-19
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3What's $n$ in the title of the question? – 2017-02-19