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BdMO Online Forum • View topic - IMO 2016 Problem 3

IMO 2016 Problem 3

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IMO 2016 Problem 3

Post Number:#1  Unread postby Phlembac Adib Hasan » Sun Aug 07, 2016 1:01 pm

Let $P=A_1A_2\cdots A_k$ be a convex polygon in the plane. The vertices $A_1, A_2, \ldots, A_k$ have integral coordinates and lie on a circle. Let $S$ be the area of $P$. An odd positive integer $n$ is given such that the squares of the side lengths of $P$ are integers divisible by $n$. Prove that $2S$ is an integer divisible by $n$.
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Re: IMO 2016 Problem 3

Post Number:#2  Unread postby Zawadx » Mon Aug 08, 2016 1:07 am

Hint for the adventurous:

Try geometric induction (jinduction)
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