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Putnam 2016 A3

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Riemann
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Putnam 2016 A3

#1

Post by Riemann » Mon Dec 05, 2016 6:04 pm

Let $f:\mathbb{R} \rightarrow \mathbb{R}$ such that

\begin{equation} f(x)+f\left(1-\frac1x\right)=\arctan x \quad \text{forall} \; x \neq 0\end{equation}

(As usual $y = \arctan x $ means $-\pi/2<y<\pi/2$ and $\tan x = y$.)

Evaluate the integral $\displaystyle \int_0^1 f(x) \, {\rm d}x$.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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