# Riemann hypothesis and diophantine equation

I read that showing Riemann hypothesis is true was equivalent to showing a particular diophantine equation doesn't have any solution.

Is there an explicit example of such a diophantine equation?

EDIT: In slides of Poonen, it is shown how DPRM theorem implies that there exists an polynomial equation that has a solution in integers if and only if the Riemann hypothesis is false. However, no explicit equation is given.

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This thread of MathOverflow should help, –  Raymond Manzoni Aug 19 '12 at 8:03

$$\forall n > 0, \left( \sum_{k \leq \delta(n)} \frac{1}{k} - \frac{n^2}{2} \right)^2 < 36n^3$$
What is $\delta(n)$? –  Seirios Aug 19 '12 at 8:18
If $\delta(n)$ is defined as in mathoverflow.net/questions/56376/recovering-n-from-sigman-n then this fails for $n=199$. –  John Bentin Dec 13 '12 at 20:49