Bangladesh IMO TST 1: 2011/ NT-1 (P 2)

For discussing Olympiad Level Number Theory problems
User avatar
Moon
Site Admin
Posts:751
Joined:Tue Nov 02, 2010 7:52 pm
Location:Dhaka, Bangladesh
Contact:
Bangladesh IMO TST 1: 2011/ NT-1 (P 2)

Unread post by Moon » Sun Mar 13, 2011 7:55 am

Problem 2:
Consider a polygon with $n$ sides. Each side has the same length $l$. The vertices of the polygon $(x_i,y_i)$ are rational coordinates, $a_i=x_{i+1}-x_i$, $b_i=y_{i+1}-y_i$, and ${a_i}^2+{b_i}^2=l^2$ for $i=1,2,\cdots,n$. Prove that $n$ is even.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

Post Reply