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One of the most famous results of Ramanujan is his formula for \(\pi\) as $$\frac{1}{\pi} =\frac{2 \sqrt 2}{\color{blue}{9801}} \sum_{k=0}^\infty \frac{(4k)!}{k!^4} \frac{29\cdot\color{blue}{70\cdot13}\,k+1103}{\color{blue}{(396^4)}^k}$$ Note that $$e^{\pi\sqrt{58}} = 396^4-104.00000017\dots$$ The terms have been factored to show some interesting connections to Pell equations. If we define the fundamental unit \(U_{29} = \frac{5+\sqrt{29}}{2}\), then
$$\big(U_{29}\big)^3=70+13\sqrt{29},\quad \text{thus}\;\;\color{blue}{70}^2-29\cdot\color{blue}{13}^2=-1$$ $$\big(U_{29}\big)^6=9801+1820\sqrt{29},\quad \text{thus}\;\;\color{blue}{9801}^2-29\cdot1820^2=1$$ $$2^6\left(\big(U_{29}\big)^6+\big(U_{29}\big)^{-6}\right)^2 =\color{blue}{396^4}$$ A similar situation happens with a pi formula using, of all things, the golden ratio. The fact that these are so has to do with the Dedekind eta function, but that's another story.