Putnam 2016 A3

Mathematical Competitions
Post Reply
User avatar
Riemann
Posts: 176
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

Putnam 2016 A3

#1

Post by Riemann »

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

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 6 guests